Energy Science Education Teaching Guide by LBenatar

Solar Energy I N S T R U C T I O N A L

M AT E R I A L S

West Valley Unified School District

WVK12-20130221

S O L A R

E N E R G Y

I N S T R U C T I O N A L

M AT E R I A L S

Solar Energy Table of Contents

Foreword

How to Use This Binder 1 Section 1 | About the Installed Solar Electric System 2 Overview 2 Background • Part 1: Electrical Energy and Power 3 Background • Part 2: How the System Works 6 Background • Part 3: Environmental Benefits 17 Experiment 21 Section 2 | Activity: Connecting Solar Panels in Series and in Parallel 22

Overview 2 2

Materials List 2 4

Background 2 5

On the Board 3 2 Multimeter Instructions 3 3 Job Assignment Sheet, Data Sheet & Worksheet 34 Section 3 | Activity: Connecting Solar Panels to a Water Pump 38

Overview 3 8

Materials List 4 0

Background 4 1 Checklist, Job Assignment Sheet & Worksheet 45

Section 4 | Math Activities 50 Overview 50 Energy Math: Obtaining Information from a Graph 51 Energy Math: Area, Multiplication, and Percentages 53 Appendix | Master Copies of Worksheets, Data Sheet, and Figures 59

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I N S T R U C T I O N A L

M AT E R I A L S

Solar Energy Foreword

These instructional materials were developed to accompany solar energy kits used for hands-on activities with students, providing teachers with background information as well as detailed instructions for the activities. If your school or site has a solar electric system installed, then data from that system may be referenced within this text. If data from your school or site were not available for inclusion within this text, then you will see generic data referenced here. These generic data are realistic but they are not actual values; they are for purposes of example only. If data from your site are not available, we encourage you to seek out schools or other sites that do have solar electric systems installed and try to gain access to their data for instructional purposes. Developing relationships of collaboration and idea exchange may be beneficial to both parties. The lessons and experiments included here expose students to real-life applications of science, technology, engineering, and math, potentially inspiring students to pursue careers in these fields. Regardless of the career paths they choose, students who learn about energy use and production benefit society by becoming better-informed citizens and consumers. Thank you for presenting these learning opportunities to your students.

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Solar Energy

How to Use This Binder

This binder contains information and activities that accompany the use of Solar Energy Kits. The contents of the binder are divided into five sections:

Section 1 | About the Installed Solar Electric System

Section 1 provides background information on energy and power, as well as fundamentals of solar cells.

Section 2 | Activity: Connecting Solar Panels in Series and in Parallel Section 2 guides you through the Connecting Solar Panels in Series and in Parallel activity, including set-‐‑up procedures, materials list, background information, instructions, and worksheets.

Section 3 | Activity: Connecting Solar Panels to a Water Pump

Section 3 guides you through the Connecting Solar Panels to a Water Pump activity, including set-‐‑up procedures, materials list, background information, instructions, and worksheets.

Section 4 | Math Activities

Section 4 provides math problems related to energy use and production.

Section 5 | Appendix

Section 5 contains master copies of all figures, worksheets, data sheets, and materials lists printed on heavier paper stock to facilitate copying for handouts and transparencies.

The goal of these activities and background information is to make the solar electric system installed at your school meaningful to students. In addition, we hope to help educators feel confident and enthusiastic when teaching students about energy use and production. Feel free to contact us with questions or comments—we value your feedback. Lisa Benatar lisa@energyscienceed.com 650.387.4990

Section 1

About the Installed Solar Electric System Overview

The goal of this section is to provide reference material so that you can be an “on-site expert” for the solar electric system installed in your district. We hope you will use this information to serve as a resource for students, staff, and visitors to the district.

This section is divided into three parts: •

Part 1 • Electrical Energy and Power provides background information on energy, its relation to power, how energy and power are measured, and how much electrical energy your school typically uses.

•

Part 2 • How the System Works describes how much power the solar electric system installed in your district provides and how the solar panels work.

•

Part 3 • Environmental Benefits discusses greenhouse gases and how they are associated with various activities such as electricity generation.

One of the additional benefits of the installed system is awareness. Having electricity generation happening on-site at a school provides a wonderful opportunity for discussion with students about where electricity comes from, how it’s used, and how it can be used more efficiently.Thank you for taking the time to learn about the system—your job as an educator adds tremendously to the value of the installation.

Section 1

About the Installed Solar Electric System Background • Part 1

Electrical Energy and Power

In today’s world, so many things we do rely on electricity. At school, we use electricity to light our rooms, run computers, keep food cold, heat food up, heat rooms, cool rooms, operate office equipment, etc.This section is designed to help you understand what energy is, how it’s measured, and how much electrical energy is typically used at your school.

Energy and Power Basics

As students witness in Section 3, Connecting Solar Panels to a Water Pump, electricity is a form of energy that can be used to perform a variety of tasks, such as operating a pump. The chemical energy stored in a log can be used for heat if we burn the log, but it cannot be used to keep us cool or power our laptops. The energy in wind, or in water at the top of a hill, or in the nucleus of an atom, becomes much more useful to us when it is converted into electricity. Electricity is a valuable form of energy that should be used wisely because there are costs, both environmental and monetary, to generating electricity. The first step in understanding how to use electrical energy wisely is to understand how much we are using. Measuring energy is tricky because energy is not something we can pick up and hold. In fact, the concept of energy as we know it today was developed fairly recently—in the early 19th century. Before that, and even somewhat further into the 19th century, scientists were grappling with this quantity that seemed to vanish, as when two moving carriages crashed into one another and both stopped moving. Our current understanding of energy evolved throughout the 19th century: we think of energy as a physical quantity that can make things happen and that can change from one form into another, but that cannot be created or destroyed.

One unit for measuring energy was developed in 1841 by the French chemist, Nicholas Clement, who defined one calorie as the amount of energy required to raise the temperature of one gram of water by one degree Celsius at atmospheric pressure. This unit can also be referred to as the gram calorie. Note: The definition of a gram calorie varies somewhat depending on the starting temperature of the water, but the variation is not significant for the purposes of this text. It should also be noted, however, that the energy content values we see on food labels in the U.S. are represented in units that are equivalent to 1,000 of the “gram calories” defined here, and so they are sometimes called food calories, big calories, kilocalories, or Calories. Food labels in Europe typically list the energy content of food in units of kilocalories to avoid confusion. When we refer to “calories” in this text, we are referring not to food calories but to gram calories.

Section 1

About the In stalled Solar Electric System

continued

Background • Part 1

Another unit for measuring energy, named after the British physicist James Prescott Joule, is the joule. One joule is equal to about 0.24 calories. This brings us to another quantity we use to help describe energy—its rate of flow. We define the rate of flow of electrical energy as electrical power, and we measure power in units called watts, where one watt (abbreviated W) is one joule per second. When we turn on a light or plug in a computer, electrons flow from the utility (or from solar panels mounted at our school site) through wires and into the appliance we are using. The rate of flow of these electrons depends on the power requirements of the appliance. A 100W incandescent light bulb requires an energy flow rate of 100 joules per second to operate. A typical compact fluorescent light bulb requires an energy flow rate of about 13 joules per second to operate. Note: For simplicity, we say in this text that electrons flow from the utility through the wires of appliances we use. While that is the case for direct current (DC) electricity, the utility provides alternating current (AC) electricity, and so electrons are actually being pushed back and forth rapidly through the wires of our appliances at a frequency of about 60 cycles per second.

When we think of electrical energy in terms of its flow rate, we can start thinking of using electrical energy in a manner similar to how we think of using water. Leaving a light on in an unoccupied room is like leaving an energy faucet of about 100 joules per second running. We can also use the water analogy to help us think about quantities of energy that are used for fixed periods of time. If we leave water running out of a faucet at a rate of 1 gallon per hour, then after 10 hours we will have used 10 gallons of water. Similarly, if we leave a light on that uses electricity at a rate of 100 joules per second, or 100 watts, then after 10 hours we will have used 100 watts times 10 hours, or 1000 watt-‐‑hours. The watt-‐‑hour is used as a unit for measuring electrical energy since it can be easily obtained by multiplying the flow rate of energy—the watt—by the amount of time that energy is flowing. When numbers get large, units of kilowatt-‐‑hours (kilo = 1,000), abbreviated kWh, are used to measure amounts of electrical energy. One kilowatt-‐‑hour is equal to about 860,000 calories.

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Background • Pcontinued art 1

About the In stalled Solar Electric System

Electricity Use in Your District

Now that we have a better sense of how energy is measured—both in terms of its rate of flow and in terms of quantities of energy—let’s take a look at how much energy is used within your school district. Table 1 shows electrical energy usage for schools where solar panels have been installed.

PLACEHOLDER • SAMPLE INFO Numbers shown here are realistic but not actual values—they are for purposes of example only.

School Arguello Elementary

2007 Electrical Energy Usage (kWh) 305,683

Number of Average U.S. Home Equivalents 27

Bacarro Elementary

230,678

Carolyne Middle

406,225

Danton Elementary Franklyn High Redington Middle

330,054

1,388,759

123

387,269

Total

3,048,668

269

Table 1: Energy usage per school at West Valley Unified School District (WVUSD) for 2007. Also shown for each site is the number of average U.S. home equivalents, assuming 11,319 kWh/year electricity usage for an average U.S. home, from EPA Greenhouse Gas Equivalencies Calculator: http://www.epa.gov/cleanenergy/ energy-resources/refs.html#houseelec.

The amount of electrical energy used by each school—especially when viewed in terms of the number of households that could be powered by that energy—can be surprising. Awareness is a first step towards action. Students, teachers, and administrators may all want to find ways to reduce electricity usage once they become aware of how much electricity is being used at school.

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Background • Pcontinued art 1

About the In stalled Solar Electric System

Generating Negawatts

The term “negawatt” was coined by physicist and energy efficiency expert Amory Lovins when he saw a typo—the “m” in the word megawatts had inadvertently been typed as an “n”—in a Colorado Public Utilities Commission report. The term stuck, and it has become a useful way to refer to reductions in power demand. Electrical power not generated matters, particularly during hours of peak electricity demand. Peak demand hours dictate how much electricity generation a utility must be equipped to supply. As the electricity flow rate demand approaches the utility’s maximum capacity to deliver electric power, the utility might choose to distribute free fluorescent light bulbs and other energy-‐‑saving measures to customers rather than to install additional generation capacity. It might prove more cost effective for the utility to generate negawatts rather than traditional megawatts produced from coal, nuclear, or gas-‐‑fired power plants. Investing in negawatts makes sense for schools as well. For example, replacing older-‐‑generation fluorescent lighting with newer lighting requires one initial investment, recaptured over time by lower utility bills. The “payback period,” or time it takes to gain back the entire initial investment, is often just a few years. Schools also benefit from reduced maintenance costs and improved reliability when energy-‐‑efficient equipment is installed. Quantitative monetary savings from energy efficiency installations are often accompanied by qualitative improvements as well. For example, energy-‐‑efficient lighting and climate control systems can be designed to provide more desirable light, room temperatures, and air quality while using less energy than conventional equipment. Thus, implementing energy efficiency measures can be a way for school districts to reduce costs and improve the learning environment. As part of the process of developing a comprehensive energy plan, your district has implemented energy efficiency measures. Table A below lists each measure, along with its associated reduction in energy use. PLACEHOLDER • SAMPLE INFO Numbers shown here are realistic but not actual values—they are for purposes of example only.

Energy Efficiency Measure

Total Annual Electricity Usage for Retrofitted Sites Prior to Retrofits (kWh)

Calculated Annual Electricity Savings Due % Electricity to Retrofits Usage Offset (kWh) by Retrofits

Lighting retrofits

3,048,668

314,012

10.3%

Pool pump replacement

1,794,984

96,929

5.4%

Table A. Estimated electricity usage offsets resulting from implementation of energy efficiency measures at West Valley Unified School District. Usage offset percents are calculated as annual electricity saved divided by total electricity used at retrofit sites.

5 b

Section 1

About the Installed Solar Electric System Background • Part 2

How the System Works Sizing the System

When a solar electric system is installed at a school site, one of the first steps is to decide on a size for the system. That size is typically based on the energy needs of the school, as well as availability of funds and space for mounting panels. Solar electric systems are typically referred to in terms of the maximum rate of flow of energy, or the maximum power, that they can provide under standard testing conditions. This is the DC kilowatt (or “DC kW”) rating under Standard Testing Conditions (STC). The amount of power the panels can provide in realistic conditions, and then the amount of energy the panels can produce over a given period of time such as a year, is calculated from the STC starting power value using factors including the availability of sunlight for a given region, temperature, shading at the installation site, tilt angle and orientation of the panels, and conversion of the electricity from direct current (DC) into alternating current (AC). Table 2 below lists the energy usage values for the schools in your district where solar has been installed, as well as the DC kW power rating for the system installed at each school site, the calculated annual energy production of the system, and the percentage of the school’s annual energy usage that the system is expected to provide. PLACEHOLDER • SAMPLE INFO Numbers shown here are realistic but not actual values—they are for purposes of example only.

School

Arguello

Elementary

2007 1st Year % of Electrical Calculated Electricity Energy Usage Production Needs Offset DC (kWh) (kWh) by System kW Installed

305,683

87.5

113,750

Bacarro Elementary

230,678

75.3

97,825

42%

Carolyne Middle

406,225

217.0

282,100

69%

Danton Elementary

330,054

211.1

274,365

83%

1,388,759

849.8

1,104,740

80%

387,269

209.3

272,090

70%

3,048,668

1,650.0

2,144,870

70%

190

Franklyn High Redington Middle Total

37%

Number of Homes That Could Be Powered by the Offset*

Table 2: Energy usage and installed solar electric system size per school where solar is installed at West Valley Unified School District.

* Assumes 11,319 kWh/year electricity usage for an average U.S. home, from EPA Greenhouse Gas Equivalencies Calculator: http://www.epa.gov/cleanenergy/energy-‐resources/refs.html#houseelec.

Section 1

Background • Part 2

About the In stalled Solar Electric System

continued

Making an Array

An electrically connected group of solar panels is referred to as a solar (or photovoltaic, or PV) array. Arrays throughout your district contribute to power production at the sites where they are installed. While the arrays installed at each site are electrically connected to their own meter or meters at that site, we refer in this text to the grouped collection of all of the arrays in the district as the district’s installed solar electric system. Table 2 above shows the calculated energy production for the solar electric system installed in your district for the first year of operation. This energy is to be produced by the solar panels installed throughout the district. Figure 1 shows a 175W solar panel as an example. For the case of this example, each solar panel measures about 5 feet by 2.5 feet, and comprises 72 single-‐‑crystalline solar cells connected in series. (See Figure 1.)

The STC maximum power output for the solar panel shown in Figure 1—175 W—is calculated as the product of the current and voltage produced by that panel, measured under standard testing conditions. In general, voltage (expressed in units of volts, abbreviated V) is the amount of energy per charge provided by a power supply. Current (expressed in units of amperes, or amps, abbreviated A) is the amount of charge per time that is delivered by the power supply. Power, as mentioned earlier in this section, is the rate of flow of energy per time, and can be expressed in units of watts, (abbreviated W). Electric power is the product of current times voltage:

electric power = current × voltage

energy time

charge time

energy charge

or, in terms of units

1 watt = 1 amp × 1 volt

When power supplies are connected in series, their voltages add together, but the current through all of the cells is the same as the current through one cell. The individual solar cells on the panel for this example are connected in series, and so the voltages produced by all of the individual cells add together. Physical characteristics of crystalline silicon are such that one single crystalline solar cell produces about 0.5 volts (or 0.5 V), and so 72 such cells connected in series produce about 36 V. The current through each cell—and therefore the current through all of the cells—for the solar panel in the example we are using is 4.9 amperes (or 4.9 A) under standard conditions. Thus the STC power output for this panel is the product of 36 V and 4.9 A, or 175 W.

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

The solar panels at a given installation are connected in series and parallel to form one or more arrays, and the current and voltage from each array are sent to an inverter. The combinations of series and parallel circuits that the panels are arranged in is designed to match the input current and voltage requirements of the inverter, which converts the power from direct current (DC, which is the type of power produced by solar cells), into alternating current (AC, which is the type of power provided by the utility). AC power is what our homes and buildings are designed to use.

Note: Within the solar industry, solar cells connected in series and packaged for mounting on a roof are commonly referred to as solar modules. The terms panel and module can be used interchangeably—the term panel is used in this text. Figure 1: A 175 W solar panel, measuring about 5 feet by 2.5 feet.

Solar panels can be mounted on shade structures, parking canopies, rooftops, sides of buildings, or ground mounts. They are oriented as closely as possible to the south given constraints of existing structures. The tilt angles for the panels vary depending on considerations of safety and power optimization. Panels (especially those mounted on vertical supports) need to be safe in the case of high winds, which means smaller tilt angles may be required. The added cost of reinforcing the mounting structures of panels installed at larger tilt angles is often prohibitive, but some tilt is useful to allow water to run off the panels, helping to keep them clean. The next section describes how to optimize panel orientation and tilt angle when possible.

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

Ideal Orientation and Tilt Angle for Solar Panels

The ideal orientation and tilt angle for solar panels position the panels so that they intercept the maximum amount of energy from the Sun and thus produce the most electrical power. Commonly, factors such as the existing orientation of a building or the presence of objects that cast shadows on planned locations for solar panels dictate the final placement of the panels. This section discusses the situation in which these outside factors do not play a role.

Panel Orientation Optimizing a solar panel’s orientation—its position relative to the north-south, east-west axes—involves knowing the Sun’s position in the sky. Most students are familiar with the idea that the Sun rises in the east and sets in the west. But they are less familiar with the position of the Sun in the middle of the day. Since the Sun’s rays hit the Earth most directly at noon, we use the Sun’s position at noon as a guide for solar panel placement. People living in the Northern Hemisphere (NH) and north of the Tropic of Cancer must look to the south to find the Sun at noon—thus, solar panels should face south in these locations. People living in the Southern Hemisphere (SH) and south of theTropic of Capricorn must look to the north to find the Sun at noon. Thus, solar panels should face north in these locations. During the summer, the Sun is higher in the sky than it is during the winter, but it is still towards the south for locations north of the Tropic of Cancer and towards the north for locations south of the Tropic of Capricorn. Note: Solar panels are sometimes mounted on sophisticated tracking systems that continually adjust the orientation or tilt angle (or both) of the panels in order to optimize electrical output. But these tracking systems add to the cost of the system, and more commonly panels are mounted onto fixed structures. It should also be noted that true south should be used for positioning solar panels. True south is different than south as determined by a compass, which is referred to as magnetic south.True south aligns with the Earth’s axis of rotation, whereas magnetic south aligns with the Earth’s magnetic field. The difference between true south and magnetic south is called magnetic declination. True south can be determined from the direction opposite to that of true north, where true north is found from the position of the North Star. True south can also be determined by noting the direction of the shadow of a vertical object at solar noon, where solar noon is the time exactly half way between sunrise and sunset. For locations in the NH and north of the Tropic of Cancer, the shadow will point to true north, and true south is the opposite direction.

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

Tilt Angle Tilt angle is another parameter that affects the amount of solar energy captured by solar panels. The ideal tilt angle for solar panels positions the panels perpendicular to the Sun’s incoming rays.This tilt angle produces the most direct angle of incidence for sunlight on the panels, which, as students see when they connect solar panels to a water pump, maximizes power output from the panels. Unfortunately, the ideal tilt angle varies for different times of the day and different times of the year. Since the most concentrated sunlight occurs at noon, we choose a tilt angle based on the Sun’s position in the sky at noon; but we still need to take into account that the Sun’s position at noon varies throughout the year. As the Earth revolves around the Sun, from our perspective (or the perspective of a solar panel), the Sun’s position in the sky at noon is highest during the summer and lowest during the winter, passing through intermediate heights at the equinoxes. Figuring out the ideal tilt angle for solar panels is complicated by the fact that there are several angles involved in the problem: 1. the angle of the tilt of the Earth’s axis 2. the angle of the latitude of the location where panels are to be installed 3. the angle of the tilt of the panels themselves As a rule of thumb, the tilt angle that represents a compromise between the value for summer and the value for winter is approximately the angle of latitude where the panels are being installed. You can understand this rule of thumb (and explain it to others) by starting with the simplified example of mounting solar panels at the equator, which removes one of the above tilt angles—the latitude angle at the equator is 0°. Once you understand this slightly simplified case, you can, by extension, understand the case of installing panels at latitudes other than 0°.

Section 1

Background • Pcontinued art 2

About the In stalled Solar Electric System

To figure out the ideal tilt angle for mounting solar panels at the equator, follow these steps:

Draw the Earth, including a line representing its intersection with the plane of its orbit around the Sun, as well as a line representing incom-‐ ing rays from the Sun at noon at the time of the Northern Hemisphere (NH) winter solstice (around December 21st). (See Figure 2.)

2. Add to your drawing a line representing the Earth’s equator and axis of rotation, labeling both, as well as the angle between the equator and the Earth’s orbital plane (23.5º, the tilt angle of the Earth’s axis). (See Figure 3.) Note that during the NH winter, the Earth’s north pole points away from the Sun.

3. Draw a solar panel mounted flat (no panel tilt) at the equator, along with a line perpendicular to the panel’s surface and a ray of incoming sunlight incident on the panel at noon. Label the angle between the line perpendicular to the panel’s surface and the incoming ray from the Sun (23.5º). (See Figure 4.)

Figure 2 intersection with orbital plane

Earth

rays from Sun at noon on Dec 21

Earth’s axis

intersection with 23.5º

Earth’s axis

Figure 3

orbital plane

rays from Sun at noon on Dec 21

solar panel mounted at equator

23.5º intersection with 23.5º

orbital plane

Figure 4

rays incident on solar panel at noon

rays from Sun at noon on Dec 21

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

Tilt Angle continued From the resulting figure—Figure 4—you should be able to see that if you are mounting solar panels at the equator and trying to optimize their performance during the winter, you should ideally face the panels towards the south and tilt them up by 23.5°.This tilt angle would position the panels perpendicular to incoming rays from the Sun.

Earth’s axis

rays from Sun at noon on June 21

To find the ideal tilt angle during the summer for panels mounted at the equator, repeat Steps 1 through 3, this time drawing incoming rays from the Sun at noon for the case of the NH summer solstice (around June 21st), as shown in Figure 5. Note that during the NH summer, the north pole points towards the Sun. As is evident from Figure 5, if you are mounting solar panels at the equator and trying to optimize their performance during the summer, you should ideally face the panels towards the north and tilt them up by 23.5°. This tilt angle would position the panels perpendicular to incoming rays from the Sun. intersection 23.5º with orbital plane

To find the ideal tilt angle during the NH spring equinox for panels mounted at the equator, repeat Steps 1 through 3 drawing the Sun’s rays at noon as solar panel mounted they would be around March 21st. For the NH spring at equator equinox, incoming rays from the Sun at noon would be perpendicular to the plane of the paper (or the Figure 5: Sun rays incident on Earth at white board). A solar panel mounted with no tilt—that summer solstice. is, flat—at the equator would be parallel to the plane of the page, and therefore perpendicular to the Sun’s rays at noon. Thus, if you are mounting solar panels at the equator and trying to optimize their performance at the NH spring equinox, you should ideally mount them flat—no tilt at all. rays incident on solar panel at noon

23.5º

A similar situation arises for the NH fall equinox, around September 21st: incoming rays from the Sun would again be perpendicular to the plane of the paper. For both equinoxes, a solar panel mounted with no tilt angle (flat) at the Earth’s equator would be perpendicular to the Sun’s rays, and thus optimized. Thus a 0° tilt, or flat mounting, is a good compromise for the tilt angle of solar panels if you live at the equator—it’s the best tilt for two points during the year (the equinoxes) and it’s halfway in between the best values for the two extremes of the year. This example at the Earth’s equator shows how a tilt angle equal to the latitude where panels are being mounted (in this case 0°) is a good compromise for panels that are mounted at a fixed tilt angle throughout the year. By extension you can imagine that solar panels mounted in the Northern Hemisphere facing south and tilted at an angle equal to the latitude of their location are perpendicular to the Sun’s rays at the equinoxes, and they are positioned in between the ideal tilt angles for summer and winter months. Sometimes solar panels are mounted at angles greater than the latitude of the panel location to optimize solar exposure during the winter if more electricity is needed in the winter compared to the summer, or at angles less than the latitude if more energy is needed in summer months. Other factors may come into play as well: for example, panels may be mounted at a different angle if they are connected to a utility grid that pays more for electricity generated during certain times of the © 2016, Energy Science Education. All rights reserved. WV-20130207

day or year, or if wind or maximum height is a consideration.

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

How Solar Cells Work

If you shine light on a solar cell, electrons are pushed towards one side of the cell and they flow if the cell is connected in a circuit. How does this happen? What pushes the electrons? The answer has to do with the clever design of a solar cell and is also related to why, if you rub your head with a balloon, it sticks.

Silicon Let’s start with the solar cell material. The most common solar cell material is silicon. Silicon is an element with an atomic number of 14, which means that it has fourteen protons in its nucleus and fourteen electrons surrounding its nucleus. As elements increase in atomic number in the periodic table, the number of protons and electrons each increases by one to make the next heavier element.The electrons arrange themselves in what are referred to as orbitals surrounding the atom’s nucleus. When an atom’s outermost orbitals are full of electrons, the atom does not readily accept, give, or even share electrons with neighboring atoms.This happens first with Helium, since its outermost orbital is full with just two electrons. After Helium, elements like to have eight electrons in their outermost orbitals. Silicon, for example, has two electrons in its innermost orbital, then 8 filling up the next orbitals, and then four electrons left over in its outermost orbitals. This leaves silicon atoms looking for four more electrons—or willing to give up the four it has— in order to have eight electrons in its outermost orbitals. When silicon forms a solid, it finds the best solution—to share. The crystal structure of silicon is a result of each silicon atom sharing its four, outermost electrons, one with each of its nearest neighbors. In this way, all of the atoms feel like they have eight outermost electrons. This sharing of electrons forms bonds between neighboring atoms. Since each atom has four electrons to share, there are four bonds. The bonds are directed outward from each atom’s nucleus. This bonding configuration gives rise to silicon’s crystal structure—which is the same as that of diamond (carbon atoms also have four outermost electrons), shown in Figure 6.

Figure 6: The crystal structure of silicon.

Single crystal silicon solar cells are made from thin slices (called wafers) of giant, cylindrical crystals of silicon (10 to 20 centimeters in diameter for solar cells) that are grown by slowly pulling a seed crystal from a crucible of molten silicon. One of the critical features of the solar cell making process is the addition of atoms other than silicon into silicon’s crystal structure. The non-silicon atoms are called dopants, and they can be added either during the crystal-growing process or afterwards, once wafers have been cut from the large cylinder.Two different elements are typically added to silicon as dopants— boron and phosphorus. The characteristics of these elements are chosen carefully to produce the desired electronic properties of the resulting material.

Section 1

About the In stalled Solar Electric System

Background • Part 2 continued

Dopants The first dopant to be added—typically to the melt from which silicon crystals are grown—is boron. Boron is an element with a total of five electrons; hence, its atomic number is 5, and it is the fifth element listed on the Periodic Table of Elements. Two electrons fill the innermost orbital of a boron atom, and three electrons are left over for bonding. Since boron only has three electrons available for bonding, when boron atoms are mixed into silicon’s crystal structure, they don’t quite fit (see Figure 7). They sit in positions where a silicon atom would be, but they only have three electrons available for bonding. The site is charge neutral—there are still the same number of protons in the nucleus of each atom as there are electrons around the nucleus. But there is a lower-energy area near the boron atom where an electron would be welcome. Because sites where boron atoms are located readily accept electrons from neighboring sites, boron (and dopants that behave like boron) is called an acceptor. If a force is applied to the electrons in the material (for example by applying a voltage across the material), electrons from neighboring sites can Hole Normal move more easily through the material because of Bond the existence of these locations that readily accept electrons. When an electron from a neighboring Boron site leaves its location and moves to the site of a atom boron atom, a positive charge is left behind at the neighboring site.This apparent motion of positive Figure 7: Boron in a silicon charge that occurs when electrons move through crystal. a material doped with acceptors leads to their description as p-‐type materials.

Section 1

About the In stalled Solar Electric System

continued

Background • Part 2

The second dopant to be added to the silicon is typically phosphorus, which has fifteen total electrons: two in its innermost orbital, eight in the next orbitals, and then five electrons in its outermost orbitals. When phosphorus atoms Normal bond are mixed into silicon’s crystal structure, they Extra don’t quite fit either (see Figure 8). They sit in unbound electron positions where a silicon atom would be, but Phosphorus they have five electrons available for bonding. atom Thus, anextraelectronislefthangingoutaround the site of the phosphorus atom, unbonded.The Figure 8: Phosphorus in a site, again, is charge neutral—the number of silicon crystal. protons in the nucleus of the phosphorus atom equals the number of electrons surrounding the nucleus. But the extra electron from each phosphorus atom is only weakly bound to the site around its atom. It can be fairly easily encouraged to leave. Atoms like phosphorus that readily give up electrons to neighboring atoms are called donors. If a force is applied to the electrons in a phosphorus-doped material, electrons from the phosphorus sites leave, resulting in negative charges moving to neighboring sites. Because donors offer negative mobile charges to a material, materials doped with donors are called n-‐type. Again, boron is typically added to the silicon crystal structure during the crystal growth process. The result is p-type silicon cylinders, which can then be sliced into p-type silicon wafers. One way that phosphorus can be introduced into the wafers is by heating the wafers and exposing them to phosphorus atoms suspended in a gas. This exposure causes the phosphorus atoms to make their way into the silicon structure, outnumbering the boron atoms in a thin layer at the wafer’s surface. The material is then cooled to lock in this layer. The critical feature of solar cells—the feature that makes them work—occurs at the boundary between the thin phosphorus top layer and the boron-doped region below.

The p-‐‑n Junction The boundary between the phosphorus-doped (n-type) layer and the boron-doped (p-type) region below is called the p-n junction. At this junction, a high concentration of weakly bound electrons (the phosphorus-doped layer) is right next to a region with almost no weakly bound electrons (the boron-doped layer). In fact, the region with almost no weakly bound electrons has lots of places that would readily accept electrons. This concentration difference, called a concentration gradient, leads to a process called diffusion. Diffusion is a net movement of things like atoms, molecules, or electrons (in this case, electrons) from areas of high concentration to areas of low concentration. The movement is driven by random thermal motions. Electrons from the n-type side of the wafer make their way over to the p-type side, where they are readily accepted by holes—or silicon bonds that are missing an electron—created by the presence of boron atoms in the crystal structure. This movement of electrons would eventually distribute electrons evenly throughout the material. As diffusion takes place, however, a force builds up to oppose further diffusion. This is the electrostatic force, the same force that makes a balloon stick to your head. © 2016, Energy Science Education. All rights reserved. WV-20130207

Section 1

Background • Part 2

About the In stalled Solar Electric System

continued

The Critical Feature — The Built-‐‑In Field An electrostatic force is present when positive and negative charges are separated. When you rub a balloon on your head, electrons from your hair are rubbed off onto the balloon because the material that balloons are made of pulls more strongly on electrons than hair does. Thus, the balloon becomes more negatively charged than your hair, and so there is an electrostatic force that pulls your hair and the balloon together. As weakly bound electrons from the phosphorus-doped layer of a solar cell wafer migrate into the boron-doped part of the wafer, they leave behind the nuclei of the phosphorus atoms that they were associated with. Since one negative charge is leaving a previously charge-balanced situation, the site of the phosphorus atom becomes positively charged once the electron leaves. Similarly, the site of the boron atom that the electron moves to becomes negatively charged. The more electrons migrate, the more charge separation occurs. An electrostatic field is built up at the p-n junction, and it exerts a force on electrons opposing further diffusion. This builtin electric field is critical to the operation of a solar cell. It is this field that pushes electrons knocked free from their atoms by sunlight to one side of the cell—the n-type side—giving them the energy to move around a circuit connected to the cell. (See Figure 9.)

incoming sunlight

Phosphorus (donor) doped silicon

n-type silicon

freed electron

built-in electric field at p-n junction

Boron (acceptor) doped silicon

p-type silicon

freed electron

Figure 9: The built-in electrostatic field at a p-n junction. Electrons freed by sun-‐ light near the p-n junction are either pushed to the n-type side (if they are freed close to the junc-‐ tion on the p-type side) or blocked from going to the p-type side directly (if they are freed on the n-type side).

The voltage that can be provided by a solar cell is a function of the pushing strength of the built-in field, and it is material-dependent. Silicon solar cells can provide about 0.5 V per cell. If more voltage is needed, individual cells can be connected in series since the voltages of cells connected in series add together. The current that a solar cell can provide depends on many factors, one of the most important being the intensity of sunlight incident on the cell, since it is the sunlight that frees electrons in the cell material. As students will see in the activity sections of this binder, increasing the intensity of sunlight incident on solar panels increases the amount of current the panels can provide. Clever design that creates a built-in field—this is what makes a solar cell work. And unlike almost all other methods for generating electricity, for solar cells the only moving parts are the electrons. © 2016, Energy Science Education. All rights reserved. WV-20130207

Section 1

About the Installed Solar Electric System Background • Part 3

Environmental Benefits

We’ve all heard how solar power avoids emission of greenhouse gases. But what are greenhouse gases, and why should we want to avoid emitting them? And why does conventionally generated electric power produce greenhouse gases?

Greenhouse Gases

To understand what a greenhouse gas is, we should first understand what is referred to as the greenhouse effect. A greenhouse is a clear structure that lets light in and then traps heat, so that temperatures inside the greenhouse increase. Certain gases in the Earth’s atmosphere, called greenhouse gases, cause heat to be trapped in the Earth’s atmosphere, so that the Earth and its atmosphere become like a greenhouse, increasing in temperature. This heating of the Earth and its atmosphere is referred to as the greenhouse gas effect. How is it that the Earth’s atmosphere lets energy in but then doesn’t let it back out? Energy from the Sun enters the Earth’s atmosphere as shorter-‐‑wavelength radiation. When that radiation is absorbed by the Earth, the Earth heats up and re-‐‑radiates energy back out into the atmosphere. But the energy radiated from the Earth is longer-‐‑wavelength radiation than the incoming radiation from the Sun. Greenhouse gases in the Earth’s atmosphere are like a one-‐‑ way filter—they allow shorter wavelengths to pass through, but they absorb longer wavelengths. Some of the radiation is re-‐‑emitted by the atmosphere back towards the Earth, and some continues to heat the atmosphere. This heat-‐‑trapping effect of greenhouse gases in our atmosphere is what keeps our Earth a comfortable, life-‐‑sustaining temperature. However, if the level of greenhouse gases in our atmosphere becomes too high, over-‐‑warming can occur. Greenhouse gases in our atmosphere include water vapor, carbon dioxide, and methane. As we’ll see below, burning hydrocarbons such as coal, oil, and natural gas, generates both water vapor and carbon dioxide. The effects of water vapor are somewhat complicated by the fact that water vapor tends to form clouds, which help reflect sunlight away from the Earth. Carbon dioxide, however, is understood to be an effective greenhouse gas. And so minimizing the burning of hydrocarbons is seen as a positive move in the effort to avoid global warming.

Section 1

About the In stalled Solar Electric System

Background • Part 3 continued

Getting from Hydrocarbons to Greenhouse Gases

Most things that we burn—wood, paper, candles, oil, gasoline, coal, natural gas—are made up of organic compounds. This doesn’t necessarily mean that they were grown without chemicals or pesticides! The word organic here means that the compound contains hydrocarbon groups—carbon atoms bonded to hydrogen atoms. Hydrocarbons sound complicated but really they’re very simple. Carbon atoms are bonded to each other in a chain, with hydrogen atoms bonded all around. The resulting structure looks something like a fully occupied dining room table where the carbon atoms represent the table and the hydrogen atoms represent people seated at the table. A molecule of octane—a hydrocarbon with eight carbon atoms—is shown in Figure 10. Methane, which is the principal com-‐‑ ponent of natural gas, is the simplest hydrocarbon, since it is one carbon atom surrounded by four hydrogen atoms. (See Figure 11.) We can demonstrate a simple example of what happens when any hydrocarbon is burned, or combined rapidly with oxygen, by looking at the chemical reaction that depicts the burning of methane, shown in Figure 12. You can see that all of the atoms in the molecules on the left side of the reaction— the reactants—are accounted for in the molecules on the right side of the reaction—the products: one carbon atom, four hydrogen atoms, and four oxygen atoms. More complicated hydrocarbons, like heating oil or gasoline, have longer chains of carbon atoms bonded to more hydrogen atoms. Burning these hydrocarbons requires more oxygen molecules, but the overall effect is the same: when a hydrocarbon is combined with oxygen (which happens when the hydrocarbon is burned), carbon dioxide and water are produced. If the burning process is not complete because not enough oxygen is available quickly enough, or if nitrogen from the air combines with the hydrocarbon, or if there are impurities such as sulfur or nitrogen present in the material being burned, other compounds such as carbon monoxide (CO), oxides of nitrogen, and oxides of sulfur may be

Figure 10: Octane, C8H18

Figure 11: Methane, CH4

Figure 12: The chemical reaction showing what happens when a hydrocarbon is burned, or combined rapidly with oxygen.

Section 1

About the In stalled Solar Electric System

Background • Part 3 continued

produced. But the principal chemical reaction, which produces carbon dioxide and water, remains. Thus, any time we burn hydrocarbons, carbon dioxide is produced. Most of the electricity generated in the world comes from burning fossil fuels—coal and natural gas—which are hydrocarbons. Solar panels produce electricity without burning hydrocarbons, and so greenhouse gas emission is avoided.

Note: Students may be interested to know that more than 99% of the electricity generated in the U.S. is produced by electric generators (as of 2006, less than 1% was generated by solar panels—plenty of room for growth!). In 1831, the Englishman Michael Faraday discovered that moving a magnet near a metal wire caused electrons in the wire to move.This discovery led to his invention of the electric generator: a magnet is spun near a coil of wire—or the coil of wire is spun relative to the magnet—and a current is generated in the wire. This device, based on one of the most fundamental forces in nature, electromagnetism, is still the basis for most electricity generation today. Power plants burn coal, natural gas, or oil to boil water to generate steam, which pushes the blades of an electric generator’s turbine, spinning a magnet near a coil of wire to produce electricity. Nuclear reactions are initiated to boil water for the same purpose. Wind blows turbines in wind farms and water flows to spin turbines at hydroelectric plants, all to move a magnet near a coil of wire.

Section 1

Background • Pcontinued art 3

About the In stalled Solar Electric System

Units for measuring carbon dioxide

Electricity produced by solar panels avoids greenhouse gas emission, but how much greenhouse gas emission would have occurred if the electricity had been generated by other means? You’ll hear many different measures of greenhouse gases: examples include tons of CO2, metric tons of CO2, pounds of CO2, as much CO2 as would be generated by a certain number of cars, as much CO2 as would be removed by planting a certain number of trees, etc. What does it all mean? So that we can get a better feel for what we as individuals can do to reduce greenhouse gas emissions, let’s look at one unit for measuring CO2: pounds. According to the U.S. Department of Energy’s Energy Information Agency (EIA), in 2005 about 120 pounds of CO2 were emitted in the United States per person per day. That figure provides us with a level to work with if we all would like to cut our own CO2 emissions by a meaningful amount. All we need to know now is how much CO2 is produced by various activities.

Driving a Car About 20 lbs. of CO2 are produced for every gallon of gasoline burned. So if your car gets 20 miles to the gallon, every mile you drive produces about 1 lb. of CO2.

Using Electricity The amount of CO2 emitted depends on how the electricity is generated. According to the EIA (using average heat rates for steam-electric generators in 2010), the number of pounds of CO2 produced by coal-fired power plants is 2.1 lbs. of CO2 per kilowatt-hour (kWh) of electricity, while natural-gas-fired power plants produce about 1.1 lbs. of CO2 per kWh. Because the manner in which electricity is produced conventionally varies by region, the associated number of pounds of CO2 emissions avoided by solargenerated electricity varies by region as well. Using the U.S. EPA’s regional map of non-baseload output emissions rates from 2009, and using California as an example, we get 0.99389 pounds of CO2 emitted per kWh of electricity generated: http://www.epa.gov/cleanenergy/documents/egridzips/eGRID2012V1_0_year09_GHGOutputrates.pdf

Non-baseload emissions rates are used because renewable energy generation is generally assumed not to affect electricity generation from power plants that run all the time, but rather that from plants whose production is dialed up and down to meet more dynamic power needs. Using this number for pounds of CO2 avoided for each kWh of electricity generated by solar panels, along with the calculated energy production for the installed solar electric system, we can calculate the number of pounds of CO2 avoided per year by the installation of the system. With values for student enrollment in your district, we can calculate this number on a per-student, per-day basis:

PLACEHOLDER • Numbers shown here are realistic but not actual values—they are for purposes of example only.

1st year calculated Pounds of CO2 Pounds of CO2 electricity production for avoided because of the avoided for each the solar electric systems Number of students installed solar electric kWh of solar-‐ at WVUSD enrolled in WVUSD for systems, generated electricity (kWh/year) school year 2008-‐09 per student per day

0.99389

2,144,870

4,816

1.2

If students in your district each try to cut their carbon emissions by 10%, or by 12 pounds of CO2 per day, just having the solar electric system installed in their district gets them closer to their goal!

Section 1

About the Installed Solar Electric System Experiment Burning Candle Oil

This simple experiment demonstrates how burning a hydrocarbon (oil) uses up oxygen and produces water (visible) and carbon dioxide (invisible).

Materials •

1 jar

•

1 oil candle

•

matches

Have students feel the inside of the jar to check if it is dry.

Explain to students that the oil of the candle is a hydrocarbon—a chain of carbon atoms bonded to hydrogen atoms—and that when we burn the oil, molecules that make up the oil combine with oxygen in the air and form carbon dioxide and water.

Put the jar over the candle and wait to see what happens. [The candle goes out.]

Ask students why they think the candle goes out.The chemical reaction of oxidation stops because one of the reactants, oxygen, is used up.

Have students feel inside the jar—water produced by the chemical reaction is condensed on the inside of the jar, so the jar should look and feel fogged up and wet.

We see the candle go out, and we can infer that oxygen was used up since we see that there is still hydrocarbon (oil) left. We can’t see the carbon dioxide, but we can assume that it replaces the oxygen, and we can see and feel the water.Thus we have evidence of the chemical reaction described as combustion of a hydrocarbon.

Figure 13: Jar over candle.

Section 2

Activity: Connecting Solar Panels in Series and in Parallel

Real-Life Application In addition to building circuits, students vary the tilt angle and orientation of solar panels to see the

Overview

This section guides the teacher through leading a classroom activity, Connecting Solar Panels in Series and in Parallel. During the activity, students practice connecting solar panels in series and parallel, and they measure the current and voltage delivered by the various panel configurations.

Basic Steps 1.

effects of changing these parameters. Thus, students

Set up a teacher’s demonstration table at the front of the classroom with the same materials that each student group will use for the activity: •

1 Solar Energy Kit (see Materials List for details)

•

1 clip-board with a copy of “Connecting Solar Panels in Series and Parallel Data Sheet” attached

series and parallel and

•

1 pencil

consider factors such as tilt angle and orientation to

•

1 copy of “Connecting Solar Panels in Series and Parallel Worksheet”

have the opportunity to connect solar panels in

derive electric power from the Sun.

2. Write the Main Ideas as well as the Activities on the board (refer to Background section). 3.

Begin with a brief explanation or review of electric circuits and their components. Explain what the day is about and demonstrate the activity (refer to Background section for details).

Divide the class into 6 to 8 groups, 4 students per group.

If you would like, assign letters A through D to the four students in each group.

Refer to the Job Assignments sheet to describe student responsibilities for this activity.

Timing

•

This activity is best done in sunny weather at midday when the Sun is near its highest point.

•

This activity requires about one hour and 30 minutes.

•

Begin with a 15-minute discussion of circuits. Allow approximately one hour for students to become familiar with the equipment and connect circuits. Allow 15 minutes for wrap-up discussion and clean up.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Overview continued

Electrical Safety The components included in the Solar Energy Kit are intended for classroom use. However, it is a good idea to provide students with basic principals of electrical safety so that they can make informed decisions when working with electrical components. According to the U.S. Government’s Center for Disease Control (CDC), the extent of injuries that result directly from electric shock (as opposed to indirectly by fire or from falling from a high place) depends on three main factors: 1. the amount of current that passes through a person 2. the path the current takes through the body 3. the duration of the current flow

For a given voltage level, the current that flows through a material depends on the electrical resistance of the material. As was stated in Section 1, voltage (expressed in units of volts) is the energy per electric charge and current (expressed in units of amperes) is the amount of charge flowing per time. Electrical resistance (expressed in units of ohms) is a measure of how strongly a material opposes the flow of electric current. The greater the resistance, the lower the current flow is for a given voltage. Human skin provides some electrical resistance, but the amount of resistance can vary greatly depending on factors such as skin thickness, dampness of the skin, and how tightly the voltage source is being gripped. Children’s skin tends to be less thick, and therefore provides less electrical resistance. Wet hands and a tight grip also reduce the resistance provided by skin. Touching voltages as low as 20 volts can be dangerous if skin is wet and its electrical resistance is very low. The following warnings are included in the laminated instruction sheet of the Solar Energy Kit:

Warning! Do not connect more than four of the type of solar panels provided in this Solar Energy Kit in series as this could result in electric shock. Warning! As a safety precaution, always make sure hands are dry before making electrical connections, even when working with low voltages. While the water pump included in this Solar Energy Kit is designed to be submerged in water, all electrical connections to the pump should be made in air to avoid contact between wet skin and sources of voltage. The first warning is intended to avoid a configuration of solar panels that could provide more than 12 volts. The second warning is intended to avoid lowering of skin resistance through contact with water. Awareness of factors that increase voltage or decrease resistance should become standard practice for students who are working with sources of electric current.

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Materials List

Solar Energy Kits, each of which includes the following materials: • • • •

1 4 1 1

wooden case with adjustable “roof” lid 3W solar panels water pump with clear tubing digital multimeter

• • • • • • • •

8 1 1 1 1 1 2 1

12-inch clip leads (white, green, or yellow) black 12-inch clip lead red 36-inch clip lead black 36-inch clip lead switch compass buckets clipboard

copies of the Connecting Solar Panels in Series and Parallel Data Sheet

pencils One copy per student of the Connecting Solar Panels in Series and Parallel Worksheet

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Background

Main Ideas 1.

An electric circuit is made up of components that provide a complete path for moving electric charges.

A series circuit provides one path for moving electric charges.

A parallel circuit provides more than one path for moving electric charges.

Activities

Measure the current and voltage from one solar panel.

Measure the current and voltage from two solar panels connected in series and parallel.

Measure the current and voltage from four solar panels connected in series.

Vary the tilt angle and orientation of panels to see effects on current and voltage.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

Electric Circuits

Students may be familiar with electric circuits from activities involving batteries, wires, and light bulbs. If students have not been exposed to electric circuits, introduce them to basic circuit concepts during this activity. If they have been exposed to electric circuits, review circuit concepts with them before the activity. This activity gives students the opportunity to apply prior knowledge of circuits and extend it to the case in which the power supply of the circuit is a solar panel instead of a battery.

Important concepts to cover to prepare students for this activity are listed below. As you discuss these concepts with students, it is helpful to have important points written on the board, along with labeled drawings. An example of helpful concepts and drawings to have on the board is given in the sheet called “On the Board: Circuits.”

Topics to cover while referring to drawings on the board: • An electric circuit provides a complete path for moving electric charges. Note: Point out the similarity between the words circuit and circle, and how both a circuit

and a circle involve a path that, when followed, brings you back to where you started.

• An electric circuit is made up of circuit components such as a power supply, conducting wires, and a load. • A power supply supplies electric charges and pushes them through the circuit. • A load is a part of an electric circuit that uses electric power. Note: A load is often referred to as a resistor in a circuit since it resists the flow of electric

charge as it converts the energy of the charges into other forms of energy such as light, heat, and motion.

• Conducting wires allow electric charges to flow through them. • A switch can be used in a circuit to open or close the conducting path. When the path is open, electric charges cannot flow. When the path is closed, electric charges can flow. • A power supply has two sides: positive and negative. The positive side is often marked with a “+” sign or connected to a red wire. The negative side is often marked with a “-“ sign or connected to a black wire. • A load has two connectors. In order for current to flow through the circuit, one connector of the load must be attached by a conducting material to the negative side of the power supply and the other connector of the load must be attached by a conducting material to the positive side of the power supply. Note: This may seem obvious but because the two connectors of electrical household

appliances are wrapped with insulation into one plug, students often don’t realize that there are two connectors coming from a load, not just one, and that they must be connected to the power supply as described above.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

The Solar Energy Kit

Students will most likely be eager to go outside and start using the equipment in the Solar Energy Kit. Introduce each of the kit’s parts to students, removing the part from the kit and providing some explanation.

Start by showing students how to open the kit’s case with the Velcro side up. Show students how the kit parts fit inside compartments. Tell them to notice where all of parts go inside the kit before removing parts so that they will know how to put items back into the kit after the activity.

The “Roof” Remove the solar panels from the case. Point out the Velcro dots on the solar panels and show students how to mount the panels onto the lid of the case, with wire leads pointing down. Be sure to point out that the two center panels should be attached to the lid first because the outer two panels will extend over the edges of the lid. Attach all four panels to the lid as a demonstration. Next show students how the angle adjuster inside the lid of the case can be positioned to prop the lid open at a tilt angle of 20, 40, or 60 degrees. Explain to students that this feature is designed to simulate the real-life situation in which solar panels are mounted on roofs or parking canopies at particular tilt angles. Throughout the activity, the lid of the case may be referred to as the “roof.” Note: You may want to mention that a more expensive way to mount solar panels is to mount them on motarized tracking devices that vary the tilt angle and orientation of solar panels to follow the Sun.

Show students the compass, which they can use to locate north, south, east and west as they orient their solar roofs during the activity. Note: Students may have experienced working with compasses while studying electricity and magnetism. You may want to remind them that a compass is a magnet that is free to rotate, and that the red end of the compass needle points north. Sometimes students are confused by the N on the compass dial, which only points north if the student rotates the compass until the N lines up with the red end of the compass needle.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

The Water Pump and Other Circuit Components Remove the water pump from the case, and explain that the water pump is the load, or the part of the circuit that uses power. Point out the two wire leads connected to the water pump. For this water pump, it does not matter which wire lead is connected to the positive side of the power supply and which is connected to the negative side. For some loads, it does matter which side of the load is connected to positive and which to negative. Remove the bundle of clip leads from the kit and explain to students that these are the conducting wires that they will use to connect the circuit components to one another. Demonstrate how to open the jaws of the clips and explain that the jaws must make contact with wire, not plastic insulation, in order for current to flow in the circuit. Point out that there are different sizes and colors of clip leads: the 12inch clip leads are intended for making connections from one solar panel to another when panels are connected in series and parallel; the long, black clip lead is intended for making connections to the negative side of the power supply (the black wire of the solar panel) and the long, red clip lead is intended for making connections to the positive side of the power supply (the red wire of the solar panel); the short, black clip lead is intended for connecting the switch to the negative (black) wire of the solar panel when the water pump is used. Remove the switch from the kit. Show students how to connect clip leads to the terminals of the switch, and how to operate the switch. Explain that the switch will be used in conjunction with the water pump in the next activity, to turn the pump on and off.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

The Solar Panels Now come back to the solar panels.You can decide how much information to share with students from Section 1: About the Installed Solar Electric System, which covers some background information about how solar cells work. For this activity, just the basics should be enough to get students started. It may be helpful to describe how solar cells work in the context of batteries, which are more familiar: • A solar cell, like a battery, is an example of a power supply. Batteries and solar cells both provide electrons, or moving charges, and a “pressure” to push the electrons through a circuit. Batteries provide the electrons and the pressure to push them using chemical reactions. Solar cells provide the electrons by using sunlight to free the electrons in the solar cell material and forces inside the solar cell material to push the electrons through the circuit. • One side of a battery is marked with a “+” and the other side is marked with a “–“. Solar cells have two wire leads: a red wire connected to the positive side and a black wire connected to the negative side. Note: Electrons leave a power supply from the negative side but the (sometimes confusing) convention is to take positive current flow to be in the direction opposite to that of electron flow since the charge on electrons is taken to be negative.

• Batteries are like a storage of “pressurized” electrons that flows when the battery is connected in an electric circuit. Solar cells provide the “pressurized” electrons only when exposed to light. • Solar cells, like batteries, can be connected in series or parallel. In fact, since one solar cell alone can only produce a limited amount of power, solar cells are typically connected together to form a solar panel, which can produce more power than a single cell. Large solar panels have been installed at your school, and small solar panels are included in the Solar Energy Kits.The solar panels installed at your school are each made of many (typically more than 50) solar cells connected in series. The solar panels in your kits are each made up of 6 solar cells connected in series. Note: You may want to show students a photo of a typical, life-size, solar panel.This photo is available in the Appendix. Alternatively, you can take students to a solar installation site for a first-hand view of the configuration of solar cells that makes up each panel.

As you discuss solar panels with students, it’s helpful to review where to look in the sky for the Sun at various times of the day and the year: • Ask students where the Sun rises and where it sets: the Sun rises in the east and sets in the west. In the Northern Hemisphere, at latitudes north of theTropic of Cancer, we look to the south to find the Sun at noon. • The Sun is higher in the sky during the summer than in the winter. Given this information, students should be able to predict whether they should face their solar panels towards the north or the south to produce the most electricity.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

The Multimeter: Measuring Current and Voltage Remove the multimeter from the kit. Explain to students that the multimeter is a device that can be used to measure multiple things: for example current and voltage. Refer to the “Multimeter Instructions” sheet to guide students through a demonstration of how to use the multimeter. After students have become familiar with the meters, give them a little more information on current and voltage. Students will be measuring the current and voltage produced by the solar panels in the Solar Energy Kit for various situations. Knowing how to measure current and voltage and how to design circuits to provide particular values of current and voltage is useful because real-world loads have particular current and voltage requirements, and so we would like to be able to design circuits to provide the current and voltage levels that match the needs of the loads. In this activity, students will see that when solar panels are connected in series, the voltage they provide increases but the current remains the same. When solar cells are connected in parallel, the current they provide increases, but the voltage remains the same. Students can see these relationships for themselves by making the measurements. Your focus should be to explain to them the basics of what current and voltage are, and how to use the multimeter. Current is a measure of the amount of electric charge per second that is flowing in a circuit. Units of current are called amperes (abbreviated amps, or A). Voltage is a measure of how much energy each of the charges has, and units of voltage are called volts (abbreviated V). The power that the solar panel can supply is the product of the current times the voltage. The power supplied by a solar cell increases either when more charges are generated or when the energy of the charges increases, or both.

Note: Electric current, voltage, and power, are often described in terms of water. Think of water being brought to the top of a hill, and then flowing down to the bottom of the hill to do some work, such as spinning a water wheel. Increasing electric current is like increasing the amount of water that is raised to the top of the hill. Increasing voltage is like increasing the height of the hill. Power is like the amount of work per time that the flowing water can accomplish at the bottom of the hill. If more water is raised to the top of the hill, or if the height of the hill is increased, more power is available at the bottom of the hill.

You can tell students that the water pump in the Solar Energy Kit was designed to operate on 12 volts and 2 amps. It can operate at lower voltage and current levels but it will pump water more slowly at these lower levels.

Instruction Sheet Show students the laminated instruction sheets in the kit, as well as the Data Sheet on the clipboard. Explain that groups will be going outside with the equipment and group members will take turns reading the instructions on the laminated instruction sheets to connect circuits, take measurements, and record data. Everyone should have the opportunity to put together a circuit.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Background continued

Ready-‐‑Set-‐‑Go!

Divide the class into 6 to 8 groups, depending on your class size, with 4 students per group. You may want to assign each student in the group a letter, A through D. Refer to the Job Assignments sheet to assign jobs to each student in the groups. Explain how the rotation will work: each letter takes a turn completing the tasks required to fill in one row of the Data Sheet table. At the end of the activity, assign clean-‐‑up jobs to students by letter. If you have time you may want to give students the Connecting Solar Panels in Series and Parallel Worksheet as a review of the activity. Most important: Have fun!

Section 2

Activity: Connecting Solar Panels in Series and in Parallel On the board: Circuits

An electric circuit is a complete path for moving electric charges. Circuit Components

Power supply: supplies power battery solar panel

Load: uses power

Conducting wires: allow current to flow open

Switch: opens or closes the conducting path of an electric circuit

Types of Circuits

simple electric circuit

series circuit: one path for moving charges

parallel circuit: more than one path for moving charges

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Multimeter Instructions

1. Draw a large picture of the multimeter on the board (see Figure 1). Refer to this drawing as you explain the various features of the multimeter to students. 2. Distribute one multimeter to each group of students. 3.

Tell students to pass the multimeter to each person in the group so that everyone has a chance to follow along with the teacher as each new feature of the multimeter is introduced.

Point out the multimeter test leads and identify the two ends of the test leads: the connector end and the probe end. The connector end connects to the multimeter, and the probe end is sharp and is used to touch items that are to be tested.

Have students make sure that the connector end of the black test lead is connected into the socket labeled “COM.”

Point out that there are two sockets at the bottom of the multimeter that can be used for the red test lead: one will be used for measuring voltage (labeled “VΩmA”) and one for measuring current (labeled “10ADC”).

Point out the dial of the multimeter and identify the three main dial positions students will need to know:

Figure 1: The multimeter

a. OFF (in the 12 o’clock position) b. 20 V

(in the upper-left quadrant)

c. 10A (in the lower-right quadrant) 8.

Have students practice turning the dial of the multimeter gently.

Have students practice setting up the multimeter to measure voltage: a. Make sure that the black test lead is connected to the socket labeled “COM.” b. Make sure the red test lead is connected to the socket labeled “VΩmA”. c. Set the dial to the 20 V

position.

d. When finished, turn the dial back to the OFF position. 10. Have students practice setting the multimeter to measure current: a. Make sure that the black test lead is connected to the socket labeled “COM.” b. Make sure the red test lead is connected to the socket labeled “10ADC”. c. Set the dial to the 10A position. d. When finished, turn the dial back to the OFF position. 11. Students should be ready to use the multimeter!

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Job Assignment Sheet

• All students assigned the letters A and B go outside and select an area for their group to perform the activity. Advise students not to get too close to another group since they don’t want to shade one another’s solar panels. • All students assigned the letter C are in charge of bringing the clipboard with the Data Sheet and a pencil outside. • All students assigned the letter D are in charge of bringing the Solar Energy Kit outside. • Once everyone in the group is outside and together with the equipment, member A begins the activity by reading the laminated instruction sheet that is part of the Solar Energy Kit and filling in the first row of the table on the Data Sheet. • After member A has measured current and voltage for one solar panel, member B follows the instructions to connect panels and measure data for the second row of the table. Students should continue in this way, taking turns setting up, taking measurements, and recording data for consecutive rows of the table on the Data Sheet until all rows have been completed. • Group members work together to add notes to the bottom of the Data Sheet.

Section 2

Data Sheet

C o n n e c t i n g Solar Panels in Series and in Parallel

Names:

Date:

Direction Panels are Facing

Panel Tilt Angle

(North or South)

(degrees, °)

Number of Panels

Date

Season

Time

40°

Series or Parallel

Voltage

Current

(S or P)

(volts, V)

(amps, I)

40°

20°

60°

40°

How does the voltage you measure from solar panels connected in series compare to the voltage you measure from one solar panel? How does the current you measure from solar panels connected in series compare to the current you measure from one solar panel? How does the voltage you measure from solar panels connected in parallel compare to the voltage you measure from one solar panel? How does the current you measure from solar panels connected in parallel compare to the current you measure from one solar panel?

Write down any other experiments you might want to try using this equipment:

Write down any questions or observations that come to mind during the experiments:

Section 2

Worksheet

C o n n e c t i n g Solar Panels in Series and in Parallel

Name:

Date:

Circle your answer to each of the following questions: 1.

In a parallel circuit, how many paths are there through which electric charges may flow? a. one b. more than one

In a series circuit, how many paths are there through which electric charges may flow? a. one b. more than one

Which of the following could be the power supply for an electric circuit? a. a wire b. a fan c. a solar cell d. a light bulb

Which of the following would use power in an electric circuit? a. a fan b. a light bulb c. a pump d. all of the above

True or False: If both wire leads coming from a motor are connected to the same side of a power supply, the motor will spin. a. True b. False

If you need at least 12 volts to operate a particular motor, how many of the 3-volt solar panels in the Solar Energy Kit would you need, and how would you connect them? a. Two panels connected in series. b. Four panels connected in series. c. Two panels connected in parallel. d. Four panels connected in parallel.

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Name:

Worksheet Answer Key

Date:

Circle your answer to each of the following questions: 1.

In a parallel circuit, how many paths are there through which electric charges may flow? a. one b. more than one

In a series circuit, how many paths are there through which electric charges may flow? a. one b. more than one

Which of the following could be the power supply for an electric circuit? a. a wire b. a fan c. a solar cell d. a light bulb

Which of the following would use power in an electric circuit? a. a fan b. a light bulb c. a pump d. all of the above

True or False: If both wire leads coming from a motor are connected to the same side of a power supply, the motor will spin. a. True b. False

Section 3

Activity: Connecting Solar Panels to a Water Pump

Overview

In the last activity, students focused on connecting solar panels in series and parallel circuits.They saw that if you want more current from an array, you should connect the panels in parallel, whereas if you want more voltage, you should connect the panels in series. Real-Life Application Students witness how the power delivered by solar panels is affected by the tilt angle of the panels, and so they see the importance of considering the tilt angle of solar panels mounted on a roof or canopy. In addition, the activity presents an opportunity for discussion

In the activity of this section, students see solar panels in action—they connect solar panels to a device that performs work, a water pump. They also vary the angle of incidence of the Sun’s rays on the solar panels to see how power delivered to the pump varies with tilt angle. This activity reinforces concepts from the previous activity since students must connect panels in series to operate the water pump. But it also introduces an additional element into the circuit—the load—and illustrates how the load converts electrical energy into other forms of energy.

Basic Steps 1.

of useful applications of solar energy in remote

Set up a teacher’s demonstration table at the front of the classroom with the same materials that each student group will use for the activity:

areas where electricity from

• 1 Solar Energy Kit (see Materials List for details)

a grid is not available.

• 1 clipboard with a copy of “Connecting Solar Panels to a Water Pump Checklist” • 1 pencil • 1 copy of “Connecting Solar Panels to a Water Pump Worksheet” 2.

Write the Main Ideas as well as the Activities on the board (refer to Background section).

Explain what the day is about and demonstrate the activity (refer to Background section for details).

Divide the class into 6 to 8 groups, 4 students per group.

Assign letters A through D to the four students in each group.

Refer to the Job Assignment Sheet to describe student responsibilities for this activity.

Timing

•

This activity is best done in sunny weather at midday when the Sun is near its highest point.

•

This activity requires about one hour.

•

Begin with a 15-minute explanation of the activity. Allow approximately 30 minutes for students to connect panels to the pump and try various tilt angles. Allow 15 minutes for wrap-up discussion and clean up.

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

Overview continued

The following warnings are included in the laminated instruction sheet of the Solar Energy Kit:

Warning! Do not connect more than four of the type of solar panels provided in this Solar Energy Kit in series as this could result in electric shock.

Warning! As a safety precaution, always make sure hands are dry before making electrical connections, even when working with low voltages. While the water pump included in this Solar Energy Kit is designed to be submerged in water, all electrical connections to the pump should be made in air to avoid contact between wet skin and sources of voltage.

The first warning is intended to avoid a configuration of solar panels that could provide more than 12 volts.The second warning is intended to avoid lowering of skin resistance through contact with water. Awareness of factors that increase voltage or decrease resistance should become standard practice for students who are working with sources of electric current.

Section 3

Activity: Connecting Solar Panels to a Water Pump Materials List

Solar Energy Kits, each of which includes the following materials: • • • •

1 wooden case with adjustable “roof” lid 4 3W solar panels 1 water pump with clear tubing 1 digital multimeter

• • • • • • • •

8 1 1 1 1 1 2 1

12-inch clip leads (white, green, or yellow) black 12-inch clip lead red 36-inch clip lead black 36-inch clip lead switch compass buckets clipboard

copies of the Connecting Solar Panels to a Water Pump Checklist

pencils One copy per student of the Connecting Solar Panels to a Water Pump Worksheet

Section 3

Activity: Connecting Solar Panels to a Water Pump Background

Main Ideas 1.

The electricity from solar panels can be used to perform useful work.

Energy cannot be created or destroyed, but it can change form.

Energy from the Sun is more concentrated when it hits a surface directly, rather than indirectly.

Activities

Connect four solar panels in series.

Use solar panels to operate an electric water pump.

Vary the tilt angle of the solar panels and observe changes in power delivered to the pump.

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

Background continued

The discussion topics of this section can be presented to students either before or after they do the Water Pump activity. Students in high school and above can probably be given the activity Checklist along with the Solar Energy Kit materials (including laminated instructions) and proceed independently. For younger students, you may want to go through the Checklist before the activity, using a Solar Energy Kit to demonstrate the activity steps. You may do the demonstration inside the classroom, without water in the buckets—just be sure that students are familiar with all parts of the kit before starting the activity.

Using Solar Energy

The Water Pump activity is meant to demonstrate for students how the electricity from solar panels can be used to perform useful tasks such as pumping water. However, as students participate in the activity, they will also gain a better understanding of what energy is, and they will have the opportunity to see how changing the angle of incidence of the Sun’s rays affects the concentration of energy from the Sun.

Energy Changes Form

Energy can be a difficult concept to grasp because it is not tangible. It is difficult to describe what energy is: its definition states that “Energy is the ability to do work.” But perhaps the most important characteristic of energy is described by the law governing its behavior, the law of conservation of energy, which says that energy cannot be created or destroyed, but it can change form. The activity of this lesson, connecting solar panels to a water pump, gives students the opportunity to witness energy changing from one form to another and doing work in the process. As students get more exposure to seeing energy take different forms, they may start to feel more comfortable with energy as a concept. Before this activity, you might want to ask students to think about energy changing forms as they participate in the activity. As they watch solar cells power a water pump, students see the solar cells convert the energy in the electromagnetic radiation from the Sun into electrical energy, which is the energy of moving electrons. Electrical energy is a very useful form of energy because it can be converted into many forms, and thus used for many things. As electric current flows through a resistor, electrons transfer some of their energy to atoms in the material of the resistor. The atoms vibrate more, thus, electrical energy is converted by a resistor into heat. If the resistance of the resistor is high enough, the resistor gets so hot that it glows, so that electrical energy is converted into light. Electric current flowing into the electromagnetic coils of a motor causes the motor to spin, so that electrical energy is converted into motion. Note: As part of this lesson, you may want to talk about some of the ways electricity is generated other than by solar cells. Refer to Section 1: About the Installed Solar Electric System, for more information.

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

Background continued

Never Look at the Sun—unless you’re a solar panel! For the Water Pump Activity, the motor of the pump is submerged in water and the pump moves water. As part of this activity, students see that changing the angle of the panels with respect to incoming rays from the Sun affects the power that the panels deliver to the pump. As you did for the last activity, Connecting Solar Panels in Series and Parallel, review with students the position of the Sun in the sky for different times of the day and different times of the year: • The Sun rises in the east and sets in the west. In the Northern Hemisphere, at latitudes north of theTropic of Cancer, we look to the south to find the Sun at noon. • The Sun is higher in the sky during the summer than in the winter. Students should notice during this activity that tilting the solar panels so that the Sun’s rays hit the panels more directly results in a greater power output from the panels. Note: This activity presents an opportunity to confirm students’ familiarity with the term “perpendicular” and the idea of a 90º angle. You may also use the terms “directly” and “indirectly” to describe how the Sun’s rays hit a surface.

As you introduce this activity to the class, go through the Checklist and make sure students understand the various parts of the Solar Energy Kit, including the angle adjustor mounted inside the lid of the kit’s case. Either before or after this activity, you may want to demonstrate, using your arm to simulate the Sun’s rays, direct incidence versus indirect incidence of the Sun’s rays on the solar panels. Note: To reinforce the relationship between the angle of incidence of incoming light and the concentration of energy delivered by the light, you may want to ask students to bring flashlights from home (or use school flashlights if they are available), and then you provide students with graph paper. Students can work in pairs to shine a beam of light on the graph paper and trace the shape that the beam illuminates on the graph paper when the flashlight is aimed directly at the paper versus indirectly. (Make sure that the distance between the paper and the flashlight remains roughly the same for both cases.) Students can count the number of squares inside the traced shape on the graph paper, and in this way they can see that when light hits a surface directly, energy from the light is concentrated into a smaller area than when light hits a surface indirectly.

As students become more familiar with direct incidence versus indirect incidence, they should be better equipped to predict the tilt angle that will produce the highest power output from the solar panels. Refer to Section 1: About the Installed Solar Electric System, for more information on optimization of tilt angle.

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

continued

Background

Connections with the Weather

This activity is also relevant to discussions of uneven heating of the Earth by the Sun. You may want to point out to students how the shape of the Earth causes the Sun’s rays to hit regions near the Equator more directly than regions near the Earth’s poles. The Earth’s surface near the Equator is like a solar panel tilted at an angle perpendicular to the incoming rays—the rays hit the surface directly. The Earth’s surface near the poles is like a solar panel tilted at an angle greater than 90º from the Sun’s rays—the rays hit the surface indirectly. Note: It is the spherical shape of the Earth that gives rise to differences in how the Earth is heated by the Sun near the Equator compared to near the poles. The tilt of the Earth’s axis is associated with variations in the concentration of the Sun’s rays at a given location for different times of the year. The tilt of the Earth’s axis also causes variations in the number of hours of daylight for a given location at different times of the year.Thus, the tilt of the Earth’s axis gives rise to seasons, but the spherical shape of the Earth gives rise to variations in heating near the Equator compared to heating near the poles.

Differences in the amount of heating for different regions of the Earth bring about temperature variations in the air and in the water. These temperature differences cause movement of air and water, which is what we experience as weather!

Section 3

Activity: Connecting Solar Panels to a Water Pump

Checklist

Name(s):

Date: Time:

1. Connect four solar panels in series. Connect the panels so that, when you are finished, the panel on the far left of the roof has a red wire hanging free and the panel on the far right of the roof has a black wire hanging free. 2. Connect one end of the red 36-inch clip lead to the free, red wire of the left-most solar panel. 3. Connect the other end of the red 36-inch clip lead to one of the wires of the water pump. It doesn’t matter which pump wire you connect to the red clip lead. 4. Connect one end of the black 12-inch clip lead to the free, black wire of the rightmost solar panel. 5. Connect the other end of the black 12-inch clip lead to one terminal of the switch. Make sure the switch is in its OPEN position. 6. Connect one end of the black 36-inch clip lead to the second terminal of the switch. 7. Connect the other end of the black 36-inch clip lead to the remaining wire of the water pump.The circuit is now connected, but the open switch is preventing current from flowing. 8. Use the roof angle adjustor to set the roof tilt angle to 40 degrees. 9. Use the compass to make sure the panels are facing South. 10. Put two buckets next to each other: one full of water, the other empty. 11. Place the water pump in the bucket full of water.

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

Checklist continued

Pour all of the water back into the pump’s bucket.

17. Close the wooden case so that the roof is flat. 18.

Close the switch. Does the pump work?

19.

Increase the roof tilt angle to 20 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower when the roof is tilted compared to when it is flat?

20.

Increase the roof tilt angle to 40 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower as you increase the tilt angle?

21. Increase the roof tilt angle to 60 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower as you increase the tilt angle? 22.

Open the switch to turn off the pump and re-fill the pump’s bucket when necessary.

23.

Change the roof’s tilt angle slowly by hand, without the roof angle adjustor, going from flat to very tilted.Try to find the ideal tilt angle, which is the tilt angle that gives the pump the most power so that water flows the fastest. Estimate the value of the ideal tilt angle:

Write down ideas for any additional experiments that you would like to try using the solar panels and the water pump:

Section 3

Activity: Connecting Solar Panels to a Water Pump Job Assignment Sheet

• All students assigned the letter A are in charge of filling up one bucket with water and carrying it outside for the activity. • All students assigned the letter B are in charge of bringing the second bucket outside. • All students assigned the letter C are in charge of bringing the Solar Energy Kit outside. • All students assigned the letter D are in charge of bringing the clipboard and pencil outside. • When following instructions of the Checklist to connect panels to the water pump, rotate through the letters A through D of your group to complete each step. Check off each step as it is completed by a group member.

Section 3

Worksheet

C o n n e c t i n g Solar Panels to a Water Pump

Name:

Date:

Answer the following questions: 1.

When the tilt angle is ideal, so that the solar panels are delivering the most power, are the Sun’s rays hitting the panels directly or indirectly?

Where do the Sun’s rays hit the Earth more directly—near the Equator, or near the poles?

What part of the Earth do you think gets heated more by the Sun—the Equator or the poles?

Do you think the ideal tilt angle for solar panels is different for different locations on the Earth?

Section 3

C o n n e c t i n g Solar Panels to a Water Pump

Worksheet Answer Key

Name:

Date:

Answer the following questions: 1.

When the tilt angle is ideal, so that the solar panels are delivering the most power, are the Sun’s rays hitting the panels directly or indirectly? When the tilt angle is ideal, the Sun’s rays hit the panels directly, which means as close to perpendicular as possible.

Where do the Sun’s rays hit the Earth more directly—near the Equator, or near the poles? The Sun’s rays hit the Earth more directly near the Equator than near the poles.

What part of the Earth do you think gets heated more by the Sun—the Equator or the poles? The Equator is heated more by the Sun than the poles because the Sun’s rays are more concentrated at the Equator.

Do you think the ideal tilt angle for solar panels is different for different locations on the Earth? Yes, the ideal tilt angle for solar panels is different for different locations on Earth. See Section 1 for details on panel tilt angle optimization.

Section 4

Math Activities Overview

The solar panels installed at your school offer a fantastic opportunity for students to have experience with real-life applications of math. Some problems are based on data from the system monitoring software, which captures real-time information such as how much electrical power is being used at the school and produced by the solar panels at the school. Other problems apply to more general aspects of solar electric installations. Most importantly, the problems presented here are a starting point— we encourage you to work with students and have them come up with questions of their own!

5 0

Section 4

Name:

Worksheet

Math A c t i v i t i e s

Your school has recently had solar panels installed.The solar panels generate electrical energy. Electrical energy can be measured in units called kilowatt-hours.

Give answers to the following questions in units of kilowatt-hours (kWh). 1. How much electrical energy did your school use yesterday?

kWh/day

2. What are the mean, median, mode, and range for the values of electrical energy used per day for the five school days at your school last week?

mode:

kWh/day

range:

kWh/day

3. What was the mean amount of electrical energy that your school used per day last weekend?

4. What is the difference between the mean amount of electrical energy used per day at your school during the week and on the weekend?

kWh/day

5. How much electrical energy did the solar panels at your school generate yesterday? kWh/day

6. What are the mean, median, mode, and range for the values of electrical energy generated per day by the solar panels at your school for the five school days last week? mean:

kWh/day

median:

kWh/day

mode:

kWh/day

range:

kWh/day

median:

kWh/day

mean:

Energy Math: Obtaining Information from a Graph

Date:

kWh/day

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Obtaining Information from a Graph continued

7. What was the mean amount of electrical energy that the solar panels at your school generated per day last weekend? kWh/day 8. What percentage of the electrical energy that your school used yesterday was generated by the solar panels? (If yesterday was not a school day, use information from the last school day.) % 9. How much energy did your school use last month? kWh/month 10. On average, in 2009 a single-family home in the U.S. consumed 11,319 kWh of delivered electricity, or about 943 kWh per month. How many average U.S. homes would it take to use the same amount of electrical energy as your school uses?

11. How many students are there at your school?

12.

How much electrical energy was used per student at your school last month? kWh/student/month

Section 4

Worksheet

Math A c t i v i t i e s

Name:

Date:

Energy Math: Area, Multiplication, and Percentages

You are a contractor who has been hired to install solar panels at a school site. You encounter the following math problems on the job.

The superintendent of the school district wants you to recommend how large of a system she should consider installing at the school site. In order to figure this out, you look at three factors:

a. Energy Demand: How much electrical energy does the school use? You don’t want to build a system that supplies more energy than the school uses. b. Available Space: How much space does the school have? You can only install as many panels as will fit on the site in places that are well-suited for solar panels. c. Budget: How much can the school spend on buying solar panels? You do not want to recommend that the school spend more money than it has available for the solar project.

In considering Energy Demand, you ask the superintendent for last year’s utility bills for the school. You add up the number of kilowatt-hours (kWh) of electrical energy for the twelve months of last year and you find that the school used 608,580 kWh total. Considering Energy Demand alone, and knowing that the school is going to try to reduce its electricity consumption by improving energy efficiency, you decide to recommend a system that produces 40% less energy in one year than the school used last year. 1. How much energy per year would a system you recommend generate, based on Energy Demand alone?

kWh

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

In considering Available Space, you visit the site and see that the best place for solar panels is the school parking lot.The lot is a good candidate for solar parking canopies, which are structures that have solar panels mounted on top of them and that shade the parking spaces beneath them. The tops of the canopies are rectangular, and each canopy can be made to cover just a few parking spaces, or an entire row of cars.You make some measurements and determine that the parking lot can accommodate ten long canopies, each one with a top mounting area that is 63 feet long and 33 feet wide. 2. If each solar panel is 5.5 feet by 3 feet, how many solar panels can fit onto the top mounting area of each canopy? Assume that the panels should be mounted so that there are no spaces between them and so that they fit exactly within the mounting area of a canopy. Sketch how you would arrange the panels on the top mounting area of each canopy. panels

Once the solar panels on each parking canopy are connected together electrically, they are referred to as an array. In considering Available Space, you need to come up with an amount of energy that each parking canopy array is likely to provide over the course of one year. Then, you need to compare that value to the amount of energy you want the completed system to provide based on the site’s Energy Demand. If you calculate that the ten parking canopy arrays that would fit at the site would produce more energy than you would recommend based on the school’s Energy Demand, then you should scale back the number of canopies that should be built. (Of course, before making a final recommendation you will also consider Budget.) In order to calculate how much energy each array is likely to produce over the course of one year, start with the power each panel is rated to provide. Solar panels are commonly referred to in terms of the DC maximum power that they provide under StandardTesting Conditions, or DC Pmax,STC.The solar panels you are using have a DC Pmax,STC rating of 230 watts each. The DC Pmax,STC rating for an array can be determined by multiplying the DC Pmax,STC rating of each panel by the number of panels in the array. 3. What is the DC Pmax,STC rating for each parking canopy array, measured in units of watts? watts 4. 1,000 watts is equal to one kilowatt (1kW). What is the DC Pmax,STC rating for each parking canopy array, measured in kW?? kW © 2016, Energy Science Education. All rights reserved. WV-20130130

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

Next, you must predict how much energy each array is likely to produce. This number of course will depend on things like weather, but an estimate can be calculated by multiplying the DC Pmax,STC rating (expressed in units of kW) for the array by a factor that accounts for things like typical weather at the school’s location, the tilt angle of the panels, and the type of inverter being used. Using a computer program that asks you for these parameter values, you determine that for this situation the factor is equal to 1400 AC kWh/DC kW/year. (Notice that the factor, when multiplied by a number of DC kilowatts, will give you a number that is in units of AC kilowatt-hours per year.) 5. Use the above factor—1400 AC kWh/DC kW/year —and the DC Pmax,STC rating for one parking canopy array to determine how much AC electrical energy one array can be expected to produce in one year AC kWh/year

6. How many parking canopies would you recommend the school build based on Energy Demand as well as Available Space? canopies

The school has a budget of one million dollars and the superintendent and school board have already determined that the dollar savings generated by the installation of solar panels makes them a good investment. 7. If each parking canopy costs $166,000 dollars to build, how many parking canopies can the school afford to build?

canopies

8. How many parking canopies would you advise the school to build, and why? canopies

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Name:

Date:

Energy Math: Area, Multiplication, and Percentages

You are a contractor who has been hired to install solar panels at a school site. You encounter the following math problems on the job.

The superintendent of the school district wants you to recommend how large of a system she should consider installing at the school site. In order to figure this out, you look at three factors:

In considering Energy Demand, you ask the superintendent for last year’s utility bills for the school. You add up the number of kilowatt-hours (kWh) of electrical energy for the twelve months of last year and you find that the school used 608,580 kWh total. Considering Energy Demand alone, and knowing that the school is going to try to reduce its electricity consumption by improving energy efficiency, you decide to recommend a system that produces 40% less energy in one year than the school used last year. 1. How much energy per yer would a system you recommend generate, based on Energy Demand alone?

365,148

kWh

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

63 ft

watts

4. 1,000 watts is equal to one kilowatt (1kW). What is the DC Pmax,STC rating for each parking canopy array, measured in kW?? 28.98

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

40,572

6. How many parking canopies would you recommend the school build based on Energy Demand as well as Available Space? 9

canopies

8. How many parking canopies would you advise the school to build, and why? I would advise the school to build 6 parking canopies because that is how many they can afford to build. Also, that number fits on the site and does not generate more energy than the school can be expected to use in one year.

canopies

9. What percentage of the energy that the school typically uses in one year would your recommended number of canopies provide? 40

Appendix

Master Copies The following pages are a compilation of all figures presented in this binder, as well as duplicates of all worksheets, data sheets and materials lists. Heavier paper stock has been used in this section to facilitate copying for classroom handouts or for making transparencies.

Section 1

F ig u re s

Section 1, Figure 1. A 175 W solar panel shown here with a Solar Energy Kit solar panel for scale.

Section 1

F ig u re s

Section 1, Figure 2

intersection with orbital plane rays from Sun at noon on Dec 21

Earth

Section 1, Figure 3

Earth’s axis

intersection with orbital plane

23.5º rays from Sun at noon on Dec 21

Section 1

F ig u re s

Section 1, Figure 4

Earth’s axis

solar panel mounted at equator 23.5º

intersection with orbital plane

rays incident on solar panel at noon

23.5º rays from Sun at noon on Dec 21

Section 1, Figure 5. Sun rays incident on Earth at summer solstice.

Earth’s axis

rays from Sun at noon on June 21

rays incident on solar panel at noon

23.5º

solar panel mounted at equator

intersection with orbital plane

Section 1

F ig u re s

Section 1, Figure 6. The crystal structure of silicon.

Normal bond

Hole Normal Bond

Boron atom Section 1, Figure 7. Boron in a silicon crystal.

Extra unbound electron

Phosphorus atom Section 1, Figure 8. Phosphorus in a silicon crystal.

Section 1

F ig u re s

incoming sunlight

Phosphorus (donor) doped silicon Boron (acceptor) doped silicon

n-type silicon

freed elect ron

built-in electric field at p-n junction p-type silicon

freed electron

Section 1, Figure 9. The built-in electrostatic field at a p-n junction. Electrons freed by sunlight near the p-n junction are either pushed to the n-type side (if they are freed close to the junction on the p-type side) or blocked from going to the p-type side directly (if they are freed on the n-type side).

Section 1

F ig u re s

Section 1, Figure 10. Octane, C8H18

Section 1, Figure 11. Methane, CH4

Section 1, Figure 12. The chemical reaction showing what happens when a hydrocarbon is burned, or combined rapidly with oxygen.

Section 1

F ig u re s

Section 1, Figure 13. Jar over candle.

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Materials List

Solar Energy Kits, each of which includes the following materials: • • • •

1 wooden case with adjustable “roof” lid 4 3W solar panels 1 water pump with clear tubing 1 digital multimeter

• • • • • • • •

8 1 1 1 1 1 2 1

12-inch clip leads (white, green, or yellow) black 12-inch clip lead red 36-inch clip lead black 36-inch clip lead switch compass buckets clipboard

copies of the Connecting Solar Panels in Series and Parallel Data Sheet

pencils One copy per student of the Connecting Solar Panels in Series and Parallel Worksheet

Section 2

Activity: Connecting Solar Panels in Series and in Parallel Background

Main Ideas 1.

An electric circuit is made up of components that provide a complete path for moving electric charges.

A series circuit provides one path for moving electric charges.

A parallel circuit provides more than one path for moving electric charges.

Activities

Measure the current and voltage from one solar panel.

Measure the current and voltage from two solar panels connected in series and parallel.

Measure the current and voltage from four solar panels connected in series.

Vary the tilt angle and orientation of panels to see effects on current and voltage.

Section 2

F ig u re s

An electric circuit is a complete path for moving electric charges.

Circuit Components

Power supply: supplies power battery solar panel

Load: uses power

Conducting wires: allow current to flow open close

Switch: opens or closes the conducting path of an electric circuit

Types of Circuits

simple electric circuit

series circuit: one path for moving charges

parallel circuit: more than one path for moving charges

Section 2

F ig u re s

Section 2, Figure 1. The multimeter.

Section 2

Data Sheet

C o n n e c t i n g Solar Panels in Series and in Parallel

Names:

Date:

Direction Panels are Facing

Panel Tilt Angle

(North or South)

(degrees, °)

Number of Panels

Date

Season

Time

40°

Series or Parallel

Voltage

Current

(S or P)

(volts, V)

(amps, I)

40°

20°

60°

40°

Write down any other experiments you might want to try using this equipment:

Write down any questions or observations that come to mind during the experiments:

Section 2

Worksheet

C o n n e c t i n g Solar Panels in Series and in Parallel

Name:

Date:

Circle your answer to each of the following questions: 1.

In a parallel circuit, how many paths are there through which electric charges may flow? a. one b. more than one

In a series circuit, how many paths are there through which electric charges may flow? a. one b. more than one

Which of the following could be the power supply for an electric circuit? a. a wire b. a fan c. a solar cell d. a light bulb

Which of the following would use power in an electric circuit? a. a fan b. a light bulb c. a pump d. all of the above

True or False: If both wire leads coming from a motor are connected to the same side of a power supply, the motor will spin. a. True b. False

Section 2

C o n n e c t i n g Solar Panels in Series and in Parallel

Worksheet Answer Key

Name:

Date:

Circle your answer to each of the following questions: 1.

In a parallel circuit, how many paths are there through which electric charges may flow? a. one b. more than one

In a series circuit, how many paths are there through which electric charges may flow? a. one b. more than one

Which of the following could be the power supply for an electric circuit? a. a wire b. a fan c. a solar cell d. a light bulb

Which of the following would use power in an electric circuit? a. a fan b. a light bulb c. a pump d. all of the above

True or False: If both wire leads coming from a motor are connected to the same side of a power supply, the motor will spin. a. True b. False

Section 3

Activity: Connecting Solar Panels to a Water Pump Materials List

Solar Energy Kits, each of which includes the following materials: • • • •

1 4 1 1

wooden case with adjustable “roof” lid 3W solar panels water pump with clear tubing digital multimeter

• • • • • • • •

8 1 1 1 1 1 2 1

12-inch clip leads (white, green, or yellow) black 12-inch clip lead red 36-inch clip lead black 36-inch clip lead switch compass buckets clipboard

copies of the Connecting Solar Panels to a Water Pump Checklist

pencils One copy per student of the Connecting Solar Panels to a Water Pump Worksheet

Section 3

Activity: Connecting Solar Panels to a Water Pump Background

Main Ideas 1.

The electricity from solar panels can be used to perform useful work.

Energy cannot be created or destroyed, but it can change form.

Energy from the Sun is more concentrated when it hits a surface directly, rather than indirectly.

Activities

Connect four solar panels in series.

Use solar panels to operate an electric water pump.

Vary the tilt angle of the solar panels and observe changes in power delivered to the pump.

Section 3

Activity: Connecting Solar Panels to a Water Pump

Checklist

Name(s):

Date: Time:

Section 3

C o n n e c t i n g S o la r Panels to a Water

Pump

Checklist continued

12. Place the free end of the water pump’s clear hose into the empty bucket, making sure that the hose is not kinked. 13. Complete the circuit by closing the switch. Does water flow? 14. Open and close the switch to turn the pump on and off. 15. Open the switch to turn the pump off. 16. Pour all of the water back into the pump’s bucket. 17. Close the wooden case so that the roof is flat. 18. Close the switch. Does the pump work? 19. Increase the roof tilt angle to 20 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower when the roof is tilted compared to when it is flat? 20. Increase the roof tilt angle to 40 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower as you increase the tilt angle? 21. Increase the roof tilt angle to 60 degrees. Listen to the sound of the pump and watch how fast the water flows. Does the water flow faster or slower as you increase the tilt angle? 22. Open the switch to turn off the pump and re-fill the pump’s bucket when necessary.

23. Change the roof’s tilt angle slowly by hand, without the roof angle adjustor, going from flat to very tilted.Try to find the ideal tilt angle, which is the tilt angle that gives the pump the most power so that water flows the fastest. Estimate the value of the ideal tilt angle:

Write down ideas for any additional experiments that you would like to try using the solar panels and the water pump:

Section 3

C o n n e c t i n g S o la r Panels to a Water

Worksheet

Pump

Name:

Date:

Answer the following questions: 1.

When the tilt angle is ideal, so that the solar panels are delivering the most power, are the Sun’s rays hitting the panels directly or indirectly?

Where do the Sun’s rays hit the Earth more directly—near the Equator, or near the poles?

What part of the Earth do you think gets heated more by the Sun—the Equator or the poles?

Do you think the ideal tilt angle for solar panels is different for different locations on the Earth?

Section 3

C o n n e c t i n g S o la r Panels to a Water

Pump

Worksheet Answer Key

Name:

Date:

Answer the following questions: 1.

Where do the Sun’s rays hit the Earth more directly—near the Equator, or near the poles? The Sun’s rays hit the Earth more directly near the Equator than near the poles.

Section 4

Name:

Give answers to the following questions in units of kilowatt-hours (kWh). 1. How much electrical energy did your school use yesterday?

kWh/day

2. What are the mean, median, mode, and range for the values of electrical energy used per day for the five school days at your school last week?

mean:

kWh/day

median:

kWh/day

mode:

kWh/day

range:

kWh/day

3. What was the mean amount of electrical energy that your school used per day last weekend? kWh/day

4. What is the difference between the mean amount of electrical energy used per day at your school during the week and on the weekend?

kWh/day

5. How much electrical energy did the solar panels at your school generate yesterday?

kWh/day

6. What are the mean, median, mode, and range for the values of electrical energy generated per day by the solar panels at your school for the five school days last week? mean:

kWh/day

median:

kWh/day

mode:

kWh/day

range:

Date:

Your school district has recently had solar panels installed. The solar panels generate electrical energy. Electrical energy can be measured in units called kilowatt-hours.

Energy Math: Obtaining Information from a Graph

Worksheet

Math A c t i v i t i e s

kWh/day

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Obtaining Information from a Graph continued

11. How many students are there at your school?

12. How much electrical energy was used per student at your school last month? kWh/student/month

Section 4

Worksheet

Math A c t i v i t i e s

Name:

Date:

Energy Math: Area, Multiplication, and Percentages

You are a contractor who has been hired to install solar panels at a school site. You encounter the following math problems on the job.

The superintendent of the school district wants you to recommend how large of a system she should consider installing at the school site. In order to figure this out, you look at three factors:

a. Energy Demand: How much electrical energy does the school use? You don’t want to build a system that supplies more energy than the school uses.

b. Available Space: How much space does the school have? You can only install as many panels as will fit on the site in places that are well-suited for solar panels. c. Budget: How much can the school spend on buying solar panels? You do not want to recommend that the school spend more money than it has available for the solar project.

1. How much energy per year would a system you recommend generate, based on Energy Demand alone?

kWh

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages

In considering Available Space, you visit the site and see that the best place for solar panels is the school parking lot. The lot is a good candidate for solar parking canopies, which are structures that have solar panels mounted on top of them and that shade the parking spaces beneath them. The tops of the canopies are rectangular, and each canopy can be made to cover just a few parking spaces, or an entire row of cars. You make some measurements and determine that the parking lot can accommodate ten long canopies, each one with a top mounting area that is 63 feet long and 33 feet wide. 2. If each solar panel is 5.5 feet by 3 feet, how many solar panels can fit onto the top mounting area of each canopy? Assume that the panels should be mounted so that there are no spaces between them and so that they fit exactly within the mounting area of a canopy. Sketch how you would arrange the panels on the top mounting area of each canopy. panels

Once the solar panels on each parking canopy are connected together electrically, they are referred to as an array. In considering Available Space, you need to come up with an amount of energy that each parking canopy array is likely to provide over the course of one year.Then, you need to compare that value to the amount of energy you want the completed system to provide based on the site’s Energy Demand. If you calculate that the ten parking canopy arrays that would fit at the site would produce more energy than you would recommend based on the school’s Energy Demand, then you should scale back the number of canopies that should be built. (Of course, before making a final recommendation you will also consider Budget.) In order to calculate how much energy each array is likely to produce over the course of one year, start with the power each panel is rated to provide. Solar panels are commonly referred to in terms of the DC maximum power that they provide under Standard Testing Conditions, or DC Pmax,STC. The solar panels you are using have a DC Pmax,STC rating of 230 watts each.The DC Pmax,STC rating for an array can be determined by multiplying the DC Pmax,STC rating of each panel by the number of panels in the array. 3. What is the DC Pmax,STC rating for each parking canopy array, measured in units of watts? watts 4. 1,000 watts is equal to one kilowatt (1kW). What is the DC Pmax,STC rating for each parking canopy array, measured in kW?? kW © 2016, Energy Science Education. All rights reserved. WV-20130130

Section 4

Worksheet

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

canopies

8. How many parking canopies would you advise the school to build, and why? canopies

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Name:

Date:

Energy Math: Area, Multiplication, and Percentages

You are a contractor who has been hired to install solar panels at a school site. You encounter the following math problems on the job.

The superintendent of the school district wants you to recommend how large of a system she should consider installing at the school site. In order to figure this out, you look at three factors:

a. Energy Demand: How much electrical energy does the school use? You don’t want to build a system that supplies more energy than the school uses.

1. How much energy per year would a system you recommend generate, based on Energy Demand alone?

365,148

kWh

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages

In considering Available Space, you visit the site and see that the best place for solar panels is the school parking lot. The lot is a good candidate for solar parking canopies, which are structures that have solar panels mounted on top of them and that shade the parking spaces beneath them. The tops of the canopies are rectangular, and each canopy can be made to cover just a few parking spaces, or an entire row of cars. You make some measurements and determine that the parking lot can accommodate ten long canopies, each one with a top mounting area that is 63 feet long and 33 feet wide. 2. If each solar panel is 5.5 feet by 3 feet, how many solar panels can fit onto the top mounting area of each canopy? Assume that the panels should be mounted so that there are no spaces between them and so that they fit exactly within the mounting area of a canopy. Sketch how you would arrange the panels on the top mounting area of each canopy. 126 panels would fit 33 ft

63 ft

Once the solar panels on each parking canopy are connected together electrically, they are referred to as an array. In considering Available Space, you need to come up with an amount of energy that each parking canopy array is likely to provide over the course of one year.Then, you need to compare that value to the amount of energy you want the completed system to provide based on the site’s Energy Demand. If you calculate that the ten parking canopy arrays that would fit at the site would produce more energy than you would recommend based on the school’s Energy Demand, then you should scale back the number of canopies that should be built. (Of course, before making a final recommendation you will also consider Budget.) In order to calculate how much energy each array is likely to produce over the course of one year, start with the power each panel is rated to provide. Solar panels are commonly referred to in terms of the DC maximum power that they provide under Standard Testing Conditions, or DC Pmax,STC. The solar panels you are using have a DC Pmax,STC rating of 230 watts each.The DC Pmax,STC rating for an array can be determined by multiplying the DC Pmax,STC rating of each panel by the number of panels in the array. 3. What is the DC Pmax,STC rating for each parking canopy array, measured in units of watts? 28,980

watts

Section 4

Worksheet Answer Key

Math A c t i v i t i e s

Energy Math: Area, Multiplication, and Percentages continued

AC kWh/year

6. How many parking canopies would you recommend the school build based on Energy Demand as well as Available Space? 9

canopies