THE ULTIMATE AS PHYSICS REVISION GUIDE
All science is either physics or stamp collecting | D.R.S
Important Physics Formulae You Need To Remember
Quantity
Symbol
S.I Unit
Formula
0
Velocity or speed
v or s
Metres/sec, m/s
S= d/t
1
Time
T
Second, s
T = d/s
2
Acceleration
a
Metres/sec², m/s²
3
Weight
W
Newtons, N
W=mxg
4
Force
F
Newtons, N
F=mxa
5
Moment
M
Newton – metres, Nm
M=Fxr
6
Work done
W
Joules, J
W = F x Δs
7
Gravitational Potential Energy
G.P.E
Joules, J
G.P.E= m x g x Δh
8
Kinetic Energy
K.E
Joules, J
KE = ½ m x v²
9
Elastic Potential Energy
E.P.E
Joules, J
10
Power
P
Watts, W
11
Density
a = Δv/t
a = F/m
E.P.E=
x Δh
P=W/t
P=F x V
Kilogram per cubic metre, kg/m³
= m/V
12
Pressure in Liquids/ Gases
P
Pascals, Pa
13 14 15
Upthrust Viscous Drag Viscosity
U F
Newtons, N Newtons, N N s/m2
16 17 18 19 20 21
Stress Strain Young Modulus Wavelength Frequency Refractive Index
22 23
Q W
Coulomb, C Joules, J
Q=Ixt W=QxV
V
Volts, V
V=IxR
25 26 27
Charge Energy transferred/work done Potential Difference Current Resistance Resistivity
28 29 30
Drift Velocity EMF Power
v
24
E λ or d f 1
I R
P
Pascals, Pa none Pascals, Pa Metres, m Hertz, Hz none
P= h x
U= W - F F= 6 rv = = F/A = Δl/l E= / V=fxλ f = 1/T (T = time period) 1
Amps, A Ohms, Ohms Meters, Metres/sec, m/s Volts, V Watts, W
xg
=
1
=
I= V/R R= V/I = (R x A) / l
P=
I= n x A x V x q =V+Ixr xR P=
/R
1|P age
SI Units Systeme International", or SI Units, is a standardised system of measurement based on internationally agreed definitions.
It has 7 Base Units, from which all other units are derived: o Metre (m) - Length o Kilogram (Kg) - Mass o Second (s) - Time o Kelvin (°K) - temperature o Ampere (A) - Current o Candela (Cd) - Luminous Intensity o Mole (mol) - Amount of a substance
All the base units have standard definition, for example, the meter is the distance travelled by light in a vacuum in
seconds.
Other units are derived from the base units. For example: -1 o Velocity (ms ) -2 o Acceleration (ms ) -2 o Density (Kgm ) Some of the derived units also have their own special unit names. For example: o Coulomb (C) - (As) Charge -1 -2 o Pascal (Pa) - (Kgm s ) Pressure 2 -3 -2 o Ohms (Ω) - (Kgm s A ) Resistance
Prefixes In order to make working with large or small numbers more convenient, a system of prefixes is used, where the unit is multiplied by a certain power of ten:
Yotta (Y) - 1024 Zetta (Z) - 1021 Exa (E) - 1018 Peta (P) - 1015 Tera (T) - 1012 Giga (G) - 109 Mega (M) - 106 Kilo (k) - 103 Milli (m) - 10-3 Micro (μ) - 10-6 Nano (n) - 10-9 Pico (p) - 10-12 Femto (f) - 10-15 Atto (a) - 10-18 Zepto (z) - 10-21 Yocto (y) - 10-24 2|P age
Contents Projectiles ............................................................................................................................................. 5 Velocity and Speed ............................................................................................................................... 6 Displacement-Time Graphs ................................................................................................................... 7 Velocity-Time Graphs ............................................................................................................................ 7 Acceleration .......................................................................................................................................... 8 Newton’s Laws of Motion ..................................................................................................................... 9 Newton’s 3rd Law Pairs .......................................................................................................................... 9 Momentum ......................................................................................................................................... 10 Types of Energy and Energy Conversions............................................................................................ 11 Work ................................................................................................................................................... 11 Power .................................................................................................................................................. 11 Energy ................................................................................................................................................. 12 Efficiency............................................................................................................................................. 12 Density ................................................................................................................................................ 14 Pressure .............................................................................................................................................. 15 Upthrust.............................................................................................................................................. 15 Moving Fluids – Streamlines ............................................................................................................... 16 Viscosity .............................................................................................................................................. 17 Terminal Velocity in a Fluid ................................................................................................................. 18 Solid Material Properties .................................................................................................................... 19 Hooke’s Law ........................................................................................................................................ 19 Elastic Strain Energy ............................................................................................................................ 20 Young’s Modulus ................................................................................................................................ 21 Law of Reflection ................................................................................................................................ 22 Refraction ........................................................................................................................................... 23 Diffraction ........................................................................................................................................... 23 The Electromagnetic Spectrum ........................................................................................................... 23 Light .................................................................................................................................................... 24 Refraction of Light .............................................................................................................................. 24 Wavefronts ......................................................................................................................................... 25 Snells Law & Refractive Index ............................................................................................................. 25 Total Internal Reflection ..................................................................................................................... 26 ............................................................................................................................................................ 27 3|P age
Polarisation ......................................................................................................................................... 27 Sound Waves ...................................................................................................................................... 28 Ultrasound .......................................................................................................................................... 29 Digital and Analogue Signals ............................................................................................................... 30 The Doppler Effect .............................................................................................................................. 31 The Principle of Superposition ............................................................................................................ 32 Interference ........................................................................................................................................ 33 Standing Waves .................................................................................................................................. 33 Path Difference ................................................................................................................................... 34 Electric Charge .................................................................................................................................... 34 Current and Circuits ............................................................................................................................ 35 Different Types of Circuits .................................................................................................................. 35 Current ................................................................................................................................................ 36 Kirchhoff’s Laws .................................................................................................................................. 36 Voltage ................................................................................................................................................ 36 E.M.F ................................................................................................................................................... 36 Power .................................................................................................................................................. 37 Measuring Voltage and Current .......................................................................................................... 37 Movement of Electrons (Drift Velocity) .............................................................................................. 38 Conduction Processes of Metal .......................................................................................................... 38 Ohm’s Law .......................................................................................................................................... 38 Resistors and Resistance ..................................................................................................................... 39 Power Dissipation in a Resistor ........................................................................................................... 39 Resistivity ............................................................................................................................................ 40 Internal Resistance ............................................................................................................................. 41 The Potential Divider .......................................................................................................................... 42 Other Circuit components .................................................................................................................. 43 Circuit Symbols ................................................................................................................................... 45
4|P age
Unit 1: Rectilinear Motion Equations Of Motion v=u+ at S=
xt
S=ut + a =
+2as
S U V A T
Displacement Initial Velocity Final Velocity Acceleration Time
S=vt - a
Projectiles
A projectile launched at an angle would continue in a straight line at a constant velocity if gravity is ignored. However, gravity makes the projectile accelerate to Earth. This shows us why a projectile launched at an angle follows a parabolic trajectory. Since the projectile is launched at an angle, it now has both horizontal and vertical velocities. The horizontal component of the velocity remains constant. The vertical component of the velocity changes as the projectile moves up or down. This is shown when looking at the vector components of the trajectory at regular time intervals. The vertical vectors decrease in magnitude due to gravity. Eventually, the effects of gravity will reduce the upward velocity to zero. This occurs at the top of the parabolic trajectory where there is only horizontal motion. After gravity reduces the upward (vertical) speed to zero it begins to add a downward velocity. This velocity increases until the projectile return to the ground. When looking at each half of the trajectory (up and down) you can determine that the speed of the projectile going up is equal to the speed of the projectile coming
5|P age
down. (Provided air resistance is ignored.) The only difference is the direction of the motion.
Vertical Component of Velocity = u sin A Horizontal Component of Velocity = u cos A
The following points should be noted. 1.
The horizontal and vertical components of a projectile launched at an angle are independent of one another.
2. The acceleration is always -9.8 directed downwards.
. The negative sign means the acceleration is
3. At the maximum height, the vertically velocity is zero. The particle may still be moving horizontally but is not moving up or down. 4. The motion of the particle is symmetric, with a vertical line of symmetry through the point of maximum height. 5. There is no horizontal acceleration so the horizontal velocity is constant: where is the initial velocity and makes with the horizontal.
is the angle the initial velocity
6. The path of a projectile is a parabola, since the equation describing projectile motion can be expressed as a quadratic. 7. Projectile motion usually assumes no air resistance, which implies the symmetrical shape.
Velocity and Speed To calculate Velocity: Velocity (Average) (m/s) = Final Velocity – Initial Velocity / Time Taken V = (V-U)/t Velocity (Instantaneous) (m/s) =
Final Velocity – Initial Velocity) / Time Taken V = (V-U)/ t
6|P age
To calculate speed: Speed (m/s) = Total Distance Moved / Time Taken s = d/t
Displacement-Time Graphs The gradient of the line tells us the velocity of the particle. The steeper the gradient, the faster the particle is moving. The picture on the right shows acceleration on a displacement-time graph.
A straight line means a steady velocity. A horizontal line means stationary. What’s the difference between speed and velocity? Velocity is speed at a particular direction.
Velocity-Time Graphs
The steeper the gradient, the greater the acceleration. The area under the line on a speed-time graph represents the distance travelled.
For the first four seconds: ½ x 4 x 8 = 16m For the next three seconds: 3 x 8 = 24m For the last three seconds: ½ x 3 x 8 = 12m Total Distance Travelled = 28+24 = 52m Or you could use the Area of Trapezium to calculate the area under the line instead of separating it into different sections.
7|P age
A= ½(a+b) x h, therefore A= ½ (3+10) x 8 = 52m
Acceleration Acceleration is the rate at which objects change their velocity. To calculate acceleration:
Acceleration (m/s2) = (Final velocity – Initial Velocity) / Time Taken A = (V-U)/t
Unit 1: Forces A force is a push or pull and squeeze or stretch of one body on another.
Force is a vector quantity. It changes in size and direction. Other examples of vector quantities include velocity, acceleration and momentum. Scalar quantities only change in size, for example, temperature. Forces are measured in newtons (N). 1kg is equivalent to about 10N. Looking at the right part of the picture above, if the forces are all equal and then cancel each other out, the forces and balanced or in Equilibrium and therefore, the unbalanced force is zero. If you look at the left picture, you can see that the forces are not equal. The skater is moving right at 120N, cancelling out the 100N. Here, there is an unbalanced force or resultant force of 120-100 = 20N.
Type of Force
What is it?
Push/Pull
A force
Friction
A force that opposes motion
Normal Reaction Force
The force that acts in an upward direction to the skater and prevents him from sinking into the ground. The pull of the Earth
Gravitational Force/Weight Air Resistance/Drag
A force that opposes the movement of objects in the air.
Upthrust
An upward push in water which is equal to the weight of the object and causes it to float. When an object is stretched, it causes it to be in a state of tension. This is when all molecular forces try and restore the object to its original length or form. To do with the attractions and repulsions between charges.
Tension
Electrostatic Force
8|P age
Newton’s Laws of Motion Newton’s 1st Law: An object will remain at rest or will continue to move in a straight line at a constant speed unless it is acted upon by an external resultant force.
Newton’s 2nd Law: The force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced. Resultant force (N) = mass (kg) x acceleration (m/s2) or F = ma
Newton’s 3rd Law: For every action there is an equal and opposite reaction If Body A exerts a force on Body B, Body B will exert an equal and opposite force on Body A.
Newton’s 3rd Law Pairs Newton’s third law pairs apply to a pair of objects. Consider the Moon orbiting the Earth.
Force of the Moon on the Earth
Force of the Earth on the Moon
The Earth exerts a gravitational force onto the moon, and the Moon exerts an equal and opposite gravitational force on the Earth. The single force on the Moon is needed to maintain its orbit around the Earth, while the force of the Moon on the Earth gives rise to the tides.
9|P age
Newton’s third law pairs must always: Act on Separate Bodies Be of the same Force type Act along the same line Be Equal in Magnitude Act in Opposite directions
Momentum Momentum is quantity possessed by masses in motion. In other words, it is a measure of how difficult it is to stop something that is moving. We can calculate it using the formula: Momentum (kg m/s) = mass (kg) x velocity (m/s) p=mxv Remember momentum is a vector quantity. Also, the rate of increase of momentum is proportional to the force applied. This leads us to: Force = change in momentum/time taken F = (mv – mu)/t Momentum is also conserved, therefore: Momentum before the collision = Momentum after the collision Collisions with no kinetic energy lost are called elastic collisions. These are usually collisions between gas molecules (they continue moving in a container and does not end up in a pile at the bottom). When a ball bounces off the ground, the collision is partially elastic – the ball rebounds, regaining its original shape, but loses some of its kinetic energy. When two objects collide and stick together, the collision is inelastic. Remember you have to consider both speeds.
Unit 1: Energy
What the hell is energy? Well, energy is used everywhere! We need to use energy to walk, to life objects, to push, to pull, and in most cases, to think. Machines also need to use energy to power up. That’s why your iPod can’t last forever without electricity! We get our energy from food and it is then transferred into other forms of energy such as kinetic energy and heat energy. What the hell are you talking about? Well you will find out later. Define Energy: Energy is the ability to do work.
10 | P a g e
Types of Energy and Energy Conversions This table summarizes some of the different types of energy that you will need to learn about in AS.
Energy
Description
Chemical
Energy that is stored in food or batteries. We burn it into other forms of energy. Also known as heat energy. Most energy is wasted by turning into this. We use thermal energy to keep ourselves warm. Also a possible form of waste energy. But I’m sure you know what sound is. It is a series of longitudinal waves – but we’ll get to that later. This energy emits a light. We need light to see things. Things like light bulbs have energy that is converted to this. Most of the energy we need is converted from electrical energy. Electrical energy can be made from other forms of energy. Stored energy that varies depending on where you are. The higher, the more. Also known as movement energy. Electrical energy is converted to kinetic energy to make motors work. We get this from chemical energy. Energy from the heat underground – stored in the Earth’s core. This is found in volcanoes and thermal springs. Energy that is stored in springs. This type of energy is found in catapults and bows. The energy released when unstable uranium atoms in the nuclear reactor break down and form a chain reaction.
Thermal Sound Light Electrical Gravitational Potential Kinetic Geothermal Elastic Potential Nuclear Energy
Energy is converted in different ways. Here are some examples:
When we run, chemical energy from our food is converted to kinetic energy. Some of it is wasted by being converted into thermal energy, making us hot. When a vibrator is used, chemical energy from the battery is converted into electrical energy, which is then converted into kinetic energy. Some is wasted through sound energy.
Work Work done is equal to energy transferred (because energy is the ability to do work). To calculate work: Work Done (joules) = Force (newtons) x Distance (metres) W=FxD Example: A weightlifter raises an object that weights 500N through a distance of 2m. Calculate the work done: W=FxD = 500N x 2m = 1000J
Power Power is the rate of transfer or energy or work. To calculate power: Power (watts) = Work Done (joules) / Time Taken (seconds) P = W/t
11 | P a g e
Energy Gravitational Potential Energy Gravitational potential energy is the energy possessed because of its position. It increases with height, if the mass and gravitational field is constant. If an object is raised above the ground, it gains GPE. Once it is dropped, the GPE turns into kinetic energy. When the object reaches the ground, all the KE is turned into heat, sound and other forms of energy. To calculate GPE: Change in GPE (joules) = Mass (kg) x Gravitational Field Strength (N/kg) x Height (m) GPE = m g h
Elastic Potential Energy Elastic potential energy is the ability of an object to do work by virtue of a change in its shape.
Change in EPE (joules) = Average Force (F) x Change in length (m) E.P.E= x Δx
Kinetic Energy Kinetic energy is movement energy. To calculate kinetic energy: KE (joules) = ½ x mass (kg) x velocity2 (m/s) KE = ½ mv2 *Note: work done = gain in GPE = gain in KE
Efficiency Energy will never disappear. It can only be wasted – or converted into other forms of energy. Physicists believe that the amount of energy in the Universe is constant – which means we cannot use energy up. This leads us to the Law of Conservation of Energy.
The Law of Conservation of Energy
Sankey Diagrams When we are considering energy transfers, we must remember that a proportion of the energy input is wasted. Real systems can never have 100% efficiency. The useful output energy will always be less than the input. Efficiency is given in percentage – usually anyway, but read the question for the specific unit.
12 | P a g e
This is a Sankey diagram. How does it work? Well the Sankey diagram always points right. The input energy is written at the beginning of the arrow, with the amount of energy specified in joules. Then the arrow splits into more arrows. The arrow that goes straight right is the useful energy (which needs to be stated too). The arrow pointing down is wasted energy. When drawing the Sankey, you need to remember several things:
All forms of energy must be stated – both the input and the output(s). The total output energy must equal to the input energy. The wasted energy slopes down. The size of the output arrows depend on their energy. As you can see, heat energy is 90 J, therefore the arrow is a lot bigger than the light energy arrow. The size also needs to be proportional – depending on the question.
To calculate efficiency: Efficiency = Useful energy output / Total energy input So in the case of the above diagram: Efficiency = 10J / 100J Efficiency = 0.1 or 10% Some Everyday Examples of Heat Loss (4.5) A filament lamp might have 5% efficiency. The other 95% is lost through heat. Nuclear power has an efficiency of 35%. The rest is lost through heat and other forms of energy. When one is running, some of his/her energy is lost through heat and friction
Unit 1: Solids, Liquids and Gases States of Matter Solids
Particles are closely packed. Regular structure. Vibrate about fixed positions.
Liquids
Particles are closely packed. Irregular structure. Random motion within structure.
Gases
No fixed positions. Move at rapid random motion. Are very spread out.
13 | P a g e
Change in States of Matter
Density Fluid/Gas
Density (kg/
) at
C
Mercury 13600 Water 1000 Air 1.24 Ethanol 790 CO2 1.78 Helium 0.161 Hydrogen 0.081 Ethylene Glycol 1.09 What’s density? Well, all solids, liquids and gases have different properties and characteristics. One such characteristic is density. Solids are often very dense, liquids are less dense than solids, and gases have very low densities. Density is how much mass something has for a certain volume – in other words, how ‘squashed up’ something is. To calculate density, use this equation: Density = Mass/Volume P = m/v Example: A piece of iron has a mass of 390kg and a volume of 0.05m3. What is its density? P = m/v P = 390kg/0.05m3 = 7800kg/m3 remember the unit! Density can be kg/m3, g/cm3…etc
Calculating Volumes for the Density For a cuboid like this, simply multiply its length, width and height. As for irregular solids, measure out a certain amount of water with a measuring cylinder. This is the control (something to compare results to). Do the same with another measuring cylinder, and drop the solid in. Note the rise in the level of water. The difference between the two measurements is the volume of the solid, in this case, 10ml.
14 | P a g e
Pressure Pressure in Solids Pressure is defined as the force per unit area. Force is measured in newtons (N) and area is measured in square meters (m2). The unit for pressure is N/m2 or Pa (for Pascals). Unfortunately, there is an equation that comes with pressure and this is ONLY FOR SOLIDS: Pressure (Pa) = Force (N)/Area (m2) P = F/a Example: A woman weighs 600N and the total area of her shoes in contact with the ground is 0.0015m 2. Find the pressure she is exerting to the ground. p = f/a p = 600N/0.0015m2 = 400000Pa (or 400kPa)
Pressure in Liquids and Gases Pressure in liquids act equally in all directions as long as the liquid is not moving, this is the same for gases. The pressure in air is a staggering 100000Pa, but since the pressure inside our bodies are similar, we don’t feel the pressure. The pressure in air is also referred to as 1.0 atmosphere. To calculate pressures in liquids use the following equation: 3
Pressure (Pa) = Height/Depth (m) x Density (kg/m ) x Gravitational Field Strength(g) Or P = h g g is usually 9.8 ms-2 Example: Rihanna’s swimming pool has a depth of 3m. What is the total pressure of the swimming pool? Take the gravitational field strength to be 10N/kg and the density of water to be 1kg/m3 (ignore the swimming pool being chlorinated ‘cause ReyReys swimming pool is always clean anyways). p=h g p = 3m x 1kg/m3 x 10N/kg p = 30Pa
Upthrust A fluid will exert an upward force on a body if it is partly or fully submerged within it. This is because the deeper into a fluid you go, the greater the weight of it and so the greater the pressure. This difference in pressure between the top and the bottom of the object produces an upward force on it. This is called Upthrust (U).
Archimedes’ Principle Archimedes' Principle states that the Upthrust on an object in a fluid is equal to the weight of the fluid displaced.
F1 = P1A =h1 gA Upthrust = Weight of Fluid Displaced F2 = P2A =h2 gA U = F2 - F1 = (h2 - h1) gA (h2 - h1) gA = V g = Mg = W 15 | P a g e
Moving Fluids – Streamlines Streamlines refer to the way a fluid travels through or over something. This includes: 1. The Flow lines 2. The Direction of the Velocity of the particles of the fluid 3. The Overall flow direction of the fluid. There are two main types of Flow, Laminar and Turbulent Flow Laminar Flow Laminar means
Planes of Lines of
Flow of Particles
Laminar Flow Properties Lines are in the same direction as the overall flow Each Lamina is in the same direction of overall flow Each Lamina has a constant individual speed All are parallel and straightish
Turbulent Flow Turbulent is different to Laminar flow as the particles act in a very random manner and although they don’t flow in the overall direction of the fluid, the majority does.
Turbulent Flow Properties Lines aren’t the same direction as the overall flow Substantial flow is in the same direction of overall fluid Turbulent flow lines have a random individual speed Flow lines are erratic/ random and create vortexes.
16 | P a g e
Viscosity In a fluid, each 'layer' exerts a force of friction on each other 'layer'. This frictional force is also present when solid object moves through a liquid. This force is called Viscous Drag. Viscous Drag is greater in Turbulent Flow than in Laminar Flow. The size of the Viscous Drag in a fluid depends on the (coefficient of) Viscosity of that fluid. Viscosity is given the letter η and is measured in Kgm-2s or Pa s. The greater the Viscosity, the greater the Viscous Drag. In most liquids, Viscosity decreases as temperature increases, whereas in most gases, Viscosity increases as temperature increases. It is therefore important to always measure the temperature of a fluid when measuring Viscosity. It is possible to calculate the drag force exerted on a spherical object in a fluid using Stoke's Law.
Stokes Law When a sphere moves slowly through a fluid, the movement of the fluid relative to the sphere is laminar. Stokes’ Law is an expression of the force in terms of the radius of the sphere (r), the velocity relative to (v), and the coefficient of Viscosity (
F = 6πηrv Stoke's Law assumes Laminar Flow, and so low velocities. In this equation, v represents Terminal Velocity. This means that the forces acting on the object are balanced. This means that is it possible to form an equation be equating Weight with Upthrust and Viscous Drag (or, in the case of Upward Motion, Upthrust with Weight and Viscous Drag).
Weight = Upthrust + Viscous Drag solid g = fluidg + 6πηrv Viscosity, η =
17 | P a g e
Terminal Velocity in a Fluid When a sphere is released and allowed to fall freely in fluid, it is subjected to three forces: its Weight (W), the Upthrust (U) and the Viscous Drag (F). As the velocity increases, the viscous drag also increases according to Stokes’ Law until U +F =W. The Resultant force then becomes zero, and the sphere continues to fall at a constant velocity known as the Terminal Velocity.
Terminal velocity, v = Terminal Velocity in Air An object moving through air experiences air resistance or drag. The size of this depends on the object’s shape and speed. Objects falling through the air experiences two significant forces: weight and drag. When an object has just been released, there is a starting velocity of 0m/s. This means there is no drag. The resulting downward acting force is just the weight force of the Earth. When it starts moving, it has a drag force acting against it, m. As the object is accelerating, it is getting faster. The faster the object moves, the bigger the drag force is.
The object then reaches a point where the drag force exactly balances the weight force. Acceleration is now at zero and the falling object is moving a constant speed. The object has reached terminal velocity.
When a skydiver jumps off the plane, she will accelerate until she reaches terminal velocity. When her parachute opens, it will cause a sudden increase in drag force. This means that there will be an unbalanced force acting upwards, causing her to decelerate. As she slows down, the drag force decreases and a new terminal velocity is reached. Or she simply forgets her parachute and dies.
Unit 1: Solid Materials Elastic and Plastic Deformation A material undergoing elastic deformation will return to its original dimensions when the deforming force is removed. A plastic material will remain deformed.
18 | P a g e
Solid Material Properties Property Hardness Stiffness
Toughness Brittleness Strength Malleability Ductility
Definition It can withstand being scratched and indents without plastic deformation A material has a high Young’s Modulus and changes its shape only slightly under large loads. A flexible material has a low Young’s Modulus and changes its shape considerably under large loads (Rubber) It is able to absorb the energy from impacts and shocks without breaking; it’s the opposite of brittle A material that gives a very small strain (little or no elastic deformation) before breaking Strength is measured by UTS (Ultimate Tensile Stress), this is the largest stress a material can withstand before breaking It can be reshaped or hammered into sheets It can be drawn into wires
Hooke’s Law Hooke's Law states that, for certain elastic materials, force is proportional to extension, when a sample is stretched. This means that the extension of the sample increases linearly with the amount of force applied. Materials that obey Hooke's law are called Hookean Materials. E.G Springs Hooke's law can be written as F = kx, where F is Force, x is extension; and k is the Stiffness Constant of the sample. The stiffness constant describes the stiffness of a material, and is measured in Nm-1.
Hooke's law can be demonstrated with the use of ForceExtension graph
However, no material follows Hooke's law indefinitely and there comes a point, called the Limit of Proportionality, where there is no longer a linear relationship between force and extension. If more force is applied, the Elastic Limit will be reached. This means that the material will no longer return to its original shape when the deforming force is removed. Eventually, if forces exceed a point called the Yield Point materials such as Copper will become Ductile and deform plastically. Forces reach a point where the material is Stressed to its maximum. This is called the UTS or simply the strength of the material. Any forces exceeding this point will cause the material to fracture and break.
19 | P a g e
Before the elastic limit is reached, the sample is experiencing Elastic Deformation, where it will return to its original shape when the load (force) has been removed. However, once the material passes that point, it experienced Plastic Deformation, where its shape is permanently changed.
Helical springs and metal wires give you a graph like the left one (except in metal wires, the graph is steeper). However, elastic bands do not obey Hooke’s Law and you get a graph like this (right).
If two springs are used in series, the effective stiffness constant of both of them is less than either of them. In fact, it can be worked out by the formula:
=
If two springs are in parallel, their effective stiffness constant is greater:
= k1 +k2 Elastic Strain Energy Up to the elastic limit of a sample, all the work done stretching has stored through potential energy, or Elastic Strain Energy. This value can be determined by calculating the area under the forceextension graph. If the sample obeys Hooke's Law, and is below the elastic limit, the Elastic Strain Energy can be calculated by the formula:
E = ½Fx or since F = kx E = ½kx2
20 | P a g e
Young’s Modulus The Young Modulus is a material property, meaning it can be applied to all samples of the same material. It is calculated by the formula:
E= /
Stress and Strain Stress is a measure of the force applied per unit cross-sectional area of a material. It is measured in Pascals (Pa), It is hence calculated by the formula:
= F/A Strain is the change in length relative to original length. It has no units since it is the ratio of two lengths. It is calculated by the formula:
= Δl/l For a material, a stress-strain graph can be drawn. The gradient of this graph is then the Young Modulus. The Young Modulus is also measured in Pascals. By finding the area under a stress-strain graph, it is possible to work out the energy stored per unit volume in a material.
Unit 2: Waves Waves transfer energy and information without transferring matter. Waves can be shown by waggling one end of a rope or slinky. It can also be shown in water using a ripple tank. The motor/oscillating paddle can be adjusted to produce vibrations that cause ripples in the water. Because of the light, these ripples can be seen under the tank. Transverse waves move at right angles to the direction of the motion of the wave. Examples include light waves and water waves. Longitudinal waves move along the direction of the motion of the wave. Examples include sound waves.
21 | P a g e
Amplitude (A) Wavelength (m) Period (s) Frequency (Hz)
Maximum movement of particles from their resting position Distance between a point on a wave and the same point on the next wave The time it takes to produce one wave The number of waves produced each second
There are two types of waves Mechanical and Electromagnetic. Mechanical waves are initiated by vibrating objects passing on some of their energy to the atoms or molecules of a material medium and therefore Mechanical waves require a medium to travel through. Electromagnetic waves are created by when charged particles are accelerated and therefore don’t require a medium to travel through. The equation for wave speed: Wave speed (m/s) = frequency (Hz) x wavelength (m) V=fxλ The equation for frequency: Frequency (Hz) = 1/time period (s) f = 1/T
Law of Reflection When waves strike a straight or flat barrier: Angle of incidence = Angle of reflection Provided the surface is smooth Note that the red line is called the normal line.
When waves strike a concave barrier, they converge.
When waves strike a convex barrier, they diverge.
22 | P a g e
Refraction Refraction is the change in speed of a wave as it travels from one medium into another where the wave direction is different. The length of the waves is altered but the frequency isn’t. When waves hit shallow water, they’ll slow down and bend towards the normal. When the waves leave the shallow water, it will bend away from the normal
Diffraction If a barrier with a large gap is placed in the path of waves, the majority of the waves passing through the gap continue in a straight line. There are regions to the left and right of the gap where there are no waves. If the size of the gap is adjusted so that it is equal to the wavelength of the water waves, they will diffract. Diffraction can also happen when waves pass a single edge. Examples of this include radio waves that are diffracted as they pass over hills.
The Electromagnetic Spectrum The electromagnetic spectrum is a continuous spectrum of waves. At one end of the spectrum, the waves have very long wavelengths. At the other end, the waves have very short wavelengths. All the waves have similar properties:
They all transfer energy They are all transverse waves They all travel at the speed of light in vacuum (300 000 000m/s) They can all be reflected, refracted and diffracted
Below is a picture that shows the order of the EM spectrum in decreasing wavelength and increasing frequency. Learn them all (except for the actual wavelengths and frequencies).
23 | P a g e
Wave Radio Waves
Microwaves
Infrared Visible Light Ultraviolet
X-rays
Gamma Rays
Uses Broadcasting and Communication – This includes television, telephone conversations, radio broadcasts… Heating food and satellite communication Heating devices and night vision cameras Used by us to see things, in photography and optical fibres Used in fluorescent lamps and sterilizing water
Observing internal structure of objects and materials and medical applications Sterilizing food and equipment as well as treat certain types of cancer
Dangers of Excessive Exposure None
Can directly heat internal body tissue – serious damage can occur before pain is felt Readily absorbed by skin and can cause skin burns None Causes skin to tan. Overexposure will lead to sunburn, blistering, skin cancer and blindness Cell mutation and cancer
Cell mutation and cancer
Light Light is a transverse wave that can be reflected, refracted and diffracted. When it strikes a flat mirror/surface, the angle of incidence = angle of reflection. The image seen in a mirror is called a virtual image. There are no rays of light actually coming from the place where the image seems to be (inside the mirror). It cannot be reproduced on screen. It’s simply a misinterpretation of the brain. The opposite of this is a real image. The image produced in a mirror is the same distance behind the mirror as the object is in front of it. It is also laterally inverted. This means when you raise your left hand, your mirror image raises his right hand. To summarize: front
The image is as far behind the mirror as the object is in The image is the same size as the object
The image is virtual The image is laterally inverted
Refraction of Light In a vacuum, light travels at around 300 000 000m/s. However, when it enters a new medium such as water, it travels more slowly and may cause a change in direction. This change in direction is called refraction. When white light passes through a prism, it emerges as a band of colours called a spectrum. It’s formed because white light is a mixture of colours and each colour
24 | P a g e
travels through the prism at a slightly different speed, so each colour is refracted by a different angle. The prism has a refractive index for each colour and as a result, each colour emerges from the prism travelling at a slightly different direction. This is called dispersion.
Wavefronts Wavefronts are an imaginary line or a surface, in the path of a wave motion, where all the displacements at any point have the same phase and an equal number of wavelengths from the source of the wave. X2
Fast
XB = V1 x t YB = V2 x t
X1 i A
i
B r
Y1
Sini =
=
Sinr =
=
Y2
Slow
r
=
x
=
Water
Snells Law & Refractive Index The relationship between the angles of incidence and refraction and the indices of refraction of the two media is known as Snell's Law. Snell's law applies to the refraction of light in any situation, regardless of what the two media are. 1
The refractive index (1 formula is:
=
) is a constant that determines the amount of refraction in a material. Its
1
=
The RF is simply a ratio between the sine of i and the sine of r, so there is no unit.
Finding the RF of a Glass Block 1. 2. 3. 4.
Set up a ray box and shine light into rectangular glass block. Measure the angle of incidence and angle of refraction. Repeat step 2 a few times. Use the formula to work out the refractive index (use deg, not radians).
25 | P a g e
Total Internal Reflection Total internal reflection occurs when a ray of light passes from an optically denser medium into an optically less dense medium such as from glass to air, the majority of the light is refracted away from the normal. However, there is a small amount that is reflected from the boundary. Total internal reflection occurs when all light is reflected from the boundary. When the incidence ray is at an angle where the refracted ray is 900 to the normal, it is called the critical angle. It is the angle at which anything bigger, and total internal reflection will occur. Its formula: n = 1/ sin c
The following points should be noted:  
When the angle of incidence is greater than the critical angle, light is refracted 900 and total internal reflection takes place. Total internal reflection only occurs from a dense medium to a less dense medium
Optical Fibres The optical fibres are very narrow, so light entering the inner core always strikes the boundary of the two glasses at an angle greater than the critical angle. Bundles of fibres carry sufficient light for images of objects to be seen through them. Optical fibres are used in endoscopes to see inside the body. It illuminates the object to be viewed.
The Prismatic Periscope Unlike normal periscopes (which use plane mirrors to reflect light), prismatic periscopes use glass prisms. Light strikes the prism at an angle greater than the critical angle for glass. The light then gets totally internally reflected twice before emerging parallel to the direction in which it was originally travelling. The final image created is sharper and brighter than those produced by a plane mirror periscope. As well as that, no multiple images will be created.
26 | P a g e
Polarisation A light wave is an electromagnetic wave that travels through the vacuum of outer space. Light waves are produced by vibrating electric charges. A light wave that is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Such light waves are created by electric charges that vibrate in a variety of directions, thus creating an electromagnetic wave that vibrates in a variety of directions. It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are a variety of methods of polarizing light.
Polarisation by Use of a Polaroid Filter The most common method of polarization involves the use of a Polaroid filter. Polaroid filters are made of a special material that is capable of blocking one of the two planes of vibration of an electromagnetic wave. In this sense, a Polaroid serves as a device that filters out one-half of the vibrations upon transmission of the light through the filter. When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light. Polarization of light by use of a Polaroid filter is often demonstrated in Physics through involving looking through Filters to view objects. The filter does not distort the shape or dimensions of the object; it merely serves to produce a dimmer image of the object since one-half of the light is blocked as it passed through the filter. A pair of filters is often placed back to back in order to view objects looking through two filters. By slowly rotating the second filter, an orientation can be found in which all the light from an object is blocked and the object can no longer be seen when viewed through two filters. What happened? In this demonstration, the light was polarized upon passage through the first filter; perhaps only vertical vibrations were able to pass through. These vertical vibrations were then blocked by the second filter since its polarization filter is aligned in a horizontal direction. While you are unable to see the axes on the filter, you will know when the axes are aligned perpendicular to each other because with this orientation, all light is blocked. So by use of two filters, one can completely block all of the light that is incident upon the set; this will only occur if the polarization axes are rotated such that they are perpendicular to each other.
27 | P a g e
The Picket Fence Analogy A picket-fence analogy is often used to explain how this dualfilter polarisation works. A picket fence can act as a polarizer by transforming an unpolarized wave in a rope into a wave that vibrates in a single plane. The spaces between the pickets of the fence will allow vibrations that are parallel to the spacing to pass through while blocking any vibrations that are perpendicular to the spacing. Obviously, a vertical vibration would not have the room to make it through a horizontal spacing. If two picket fences are oriented such that the pickets are both aligned vertically, then vertical vibrations will pass through both fences. On the other hand, if the pickets of the second fence are aligned horizontally, then the vertical vibrations that pass through the first fence will be blocked by the second fence.
Sound Waves Sound waves are longitudinal waves that travel through gases, liquids and solids. They travel slower in air, at around 340m/s and faster in solids. Sound waves cannot travel in vacuum. Sound waves can be reflected, refracted and diffracted. Frequency Range for Humans: 20Hz – 20 000Hz (hertz)
Measuring the Speed of Sound 1.
Stand 50m away from a large, blank wall and clap wood blocks. Listen for an echo. Set up a rhythm of claps so that the echo comes exactly between two claps. Ask a friend to time 20 claps. During this time, sound has travelled 2000m (to the wall and back 20 times). Divide this distance by the time to work out the speed of sound.
2.
Turn on the single generator so it produces a known frequency (such as 1 kHz). Move the microphones so that the two waves that form on the oscilloscope are exactly on top of each other. This would show that the microphones are at 1 wavelength away from each other. Measure the distance between the microphones. The speed of sound can be worked out using
28 | P a g e
the formula v = f x λ An image of a sound wave produced in a oscilloscope will look like this: To determine the frequency of a sound wave, find the time period for one complete wave and use the relationship f = 1/T to find calculate the frequency.
The loudness of a sound depends on the amplitude of the vibration (of the waves). The pitch of the sound depends on the frequency of the vibration.
Letter P Q R S
Description High pitched, loud Low pitched, soft High pitched, soft Low pitched, soft The higher the frequency, the higher the pitch. The higher the amplitude, the louder the sound.
Ultrasound Ultrasound describes sound waves of the frequency greater than the upper threshold of human hearing (about 20 kHz).
Ultrasound & Medicine In medicine frequencies in the range of 1-3 MHz are used for medical images. Sound is a wave it has all the usual wave properties (reflection, refraction, diffraction). Ultrasound imaging makes use of the fact that sound can be reflected. The idea is just like that used in radar and sonar.
Uses of Ultrasound in Medicine
Ultrasound is used for examining soft tissue inside the body. Parts of the body that may be examined include muscles and unborn babies. Blood flow can also be monitored using ultrasound.
Why Ultrasound is Safer than X-Rays Ultrasound is very safe. There is no firm evidence that it does any harm to the body since the waves used to image babies and tissue have very small amplitude and so low energy. This means there is no damage done to any living cells.
29 | P a g e
X-rays are potentially dangerous. X-rays are high energy electromagnetic waves, which have enough energy to damage or kill human cells. This makes them particularly harmful to young children and pregnant women.
A-Scans Amplitude scans (A-scans) are used to determine the depth of boundaries between tissues or bone and tissue.
A thin layer of jelly is placed between the probe and the skin to make sure all the sound enters the body. The probe contains a transmitter and a receiver. A pulse of ultrasound is sent out by the transmitter. The pulse is reflected from a surface and returns to the receiver. The ultrasound machine measures how long it takes for the pulse to return
The reflections from the outer skin layer to the inner tissue or bones are shown on the screen of a CRO. The time between the reflections and the entry of the pulse can be measured using the time base of the CRO and the depth of the boundaries are calculated using the pulse-echo formula.
x= Where X is the distance, V is the velocity of the wave and t is the time taken. Since Millions of sound waves are transmitted every second. The waves are reflected at different times, the computer in the ultrasound machine calculates how far the wave travelled before being reflected (using x = ). Using this information the computer builds up an image of the inside of the patient. Modern ultrasound equipment can produce 3D images, Colour enhancement to show blood flow and Digital files for examination on computers.
Digital and Analogue Signals When telephones, fax-machines and internet-linked computers transmit information, they must convert the information into a stream of electrical/light pulses. These pulses carry information as analogue or digital signals. Digital Signal Analogue Signal
Information is converted into a sequence of 0s and 1s called a binary code. These numbers are then converted into a series of electrical pulses. Information is converted into electrical voltages or currents that vary continuously.
30 | P a g e
Advantages of Using Digital Signals All signals become weaker during transmission as they lose energy or they pick up unwanted signals such as interference or noise. As a result, signals need to be amplified. Regeneration of digital signals creates a clean, accurate copy of the original signal as it simply restores their distinct ‘0’ and ‘1’ shape. On the other hand, when analogue signals are amplified, any accompanying noise is also amplified. These unwanted noises may drown out the original signal or introduce errors in the information being carried.
Digital signals can be made very short so more pulses can be carried around per second, meaning more information is passed on.
The Doppler Effect The Doppler Effect is a change in frequency due to relative motion. The Doppler Effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer when the source is approaching and an apparent downward shift in frequency for the observer and the source is receding or moving further away. The Doppler Effect can be observed to occur with all types of waves - most notably water waves, sound waves, and light waves.
The Doppler Effect is observed because the distance between the source of sound and the observer is changing. When the source approaches the observer, then the distance between them decreases and when the source moves away from the observer, then the distance increases. The source of sound always emits the same frequency. Therefore, for the same period of time, the same number of waves must fit between the source and the observer. If the distance is large, then the waves can be spread apart; but if the distance is small, the waves must be compressed into the smaller distance. For these reasons, if the source is moving towards the observer, the observer perceives sound waves reaching him or her at a more frequent rate (high pitch). And if the source is moving away from the observer, the observer perceives sound waves reaching him or her at a less frequent rate (low pitch).
31 | P a g e
It is important to note that the effect does not result because of an actual change in the frequency of the source. The source emits the same frequency; the observer only perceives a different frequency because of the relative motion between them. The Doppler Effect is a shift in the apparent or observed frequency and not a shift in the actual frequency at which the source vibrates.
We are most familiar with the Doppler Effect because of our experiences with sound waves. An example of this effect is in which a police car or emergency vehicle was traveling towards you on the road. As the car approached with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency) was high; and then suddenly after the car passed by, the pitch of the siren sound was low. That was the Doppler Effect - a shift in the apparent frequency for a sound wave produced by a moving source.
The Principle of Superposition Superposition occurs when two or more waves meet, a simple example: It looks like nothing happened, in actual fact at the very instant the waves passed one another their displacements combined, cancelling out, leaving no wave at all before carrying on their way again. In general the principle of superposition is that: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location. Displacement of Pulse 1 +1 -1 +1 +1
Displacement of Pulse 2 +1 -1 -1 -2
= = = = =
Resulting Displacement +2 -2 0 -1
The 3 basic rules you need to remember:
peak + peak = 'superpeak'
trough + trough = 'supertrough'
peak + trough = no displacement
32 | P a g e
Interference Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium. Constructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses. Constructive interference is observed at any location where the two interfering waves are displaced upward. But it is also observed when both interfering waves are displaced downward. This is shown in the diagram below for two downward displaced pulses. Destructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. In the diagram above, the interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting displacement of the particles of the medium.
Coherent Sources Coherent sources have the same frequency and maintain a constant phase relationship.
Standing Waves Standing (or stationary) waves are waves where the positions of the peaks and troughs do not move. You can observe standing waves by fixing one end of a piece of rope to a stationary object and oscillating it like a sin wave. When the wave reaches the fixed when it 'reflects' back towards you. When this occurs fast enough you'll start to see standing wave patterns like the diagram to the left. By changing the frequency different patterns can be observed: As mentioned standing waves get their name because they do not appear to move. What is actually happening is that two identical waves are travelling in opposite directions because of the fixed end(s).
33 | P a g e
Nodes and Antinodes
In the context of standing waves, a node is a point where the amplitude is zero. An antinode is the opposite: a point where the amplitude is at its maximum:
Path Difference Path difference is the difference (in meters) between the lengths of two paths. When two waves have the same frequency, and travel at the same velocity, and travel the same distance they will keep the same phase difference. But, if one of the waves has to travel a longer path its phase will be retarded by the time it gets to the same point as a wave travelling the more direct path. Path difference = S2P – S1P = n Where n = the order of the maximum from the centre. Example: In an experiment using microwaves, the position of the fourth maximum from the centre was 48 cm from one slit and 60cm from the other. Calculate the wavelength of the waves. Path difference = 60cm-48cm = 12cm 12cm = 4
Unit 2: Electricity Unit Ampere (A) Coulomb (C) Joule (J) Ohm (Ω) Second (s) Voltage (V) Watt (W)
What It Measures Current (I) Charge (Q) Energy (E) Resistance (R) Time (t) Volts (V) Power (P)
Electric Charge Insulating materials can be given an electric charge by rubbing them –or charging by friction. This does not create charge, but separates them.
When two uncharged insulators (a plastic rod and a cloth) are rubbed together, electrons from the rod would be rubbed onto the cloth, making the cloth negatively charged and the rod positively charged. Remember, it’s the electrons that move, not protons. Also remember:
Like forces attract Unlike forces repel
34 | P a g e
Electrostatic Phenomena: When electrons are rubbed onto insulating materials, charging them up, and therefore, making them repel or attract other objects.
Current and Circuits Explaining Charge, Current and Voltage Meet Mr.Coulomb: Mr. Coulomb is a single charge. He carries voltage, emptying it for his fellow light bulbs, arriving at the batteries to take more voltage until it runs out. Current is the rate of flow of charge. If we have 9 Mr. Coulombs running around at once then that’s our current.
To calculate charge: Charge (C) = Current (A) x Time (s) Q=Ixt
Indicating the Presence of a Current Lamps and LEDs (light emitting diodes) will glow when there is a current flowing in the circuit.
Different Types of Circuits Series Circuits In a series circuit, current is the same throughout the circuit. The size of the current depends on the voltage supplied and the number and nature of the other components in the circuit. If more bulbs are added, there will be a greater resistance throughout the circuit. In a series circuit, the total resistance is the resistance of all the other resistors added up. One switch can turn on all the components together. If there is a fault in the circuit, the whole thing stops working. Voltage is shared between all the components – the more bulbs added the dimmer they become. The larger the resistance of the component, the bigger its share of voltage. Decorative lights (the ones you put on Christmas trees) are wired in series.
Parallel Circuits Parallel circuits have branches so there are more paths for the current to flow. This means that it is possible to turn different parts of the circuit on or off by using switches. The voltages across components in a parallel circuit are all equal. Current however, halves at every junction.
Switches can be placed to switch individual bulbs or switch them all on together. If one bulb breaks, only the other components from the same branch would break.
35 | P a g e
If more bulbs are added, since voltage is the same, all bulbs will be equally bright – however, voltage runs out quicker. Lights in your home are wired in parallel.
Current Current (I) is the rate of flow of Charge Carriers, such as electrons. Current moves in the direction of negative to positive, since in metals it is electrons that carry electric charge.
I=
,
=Ix
Current (I) is the amount of Charge, Q that passes a point in a set time, t. It is measured in Amps (A), and charge is measured in Coulombs (C). Since Amps are SI base units, Coulombs are defined as A × s, As.
Kirchhoff’s Laws Kirchhoff’s 1st Law Current entering a component or junction will always be the same as the current leaving.
Kirchhoff’s 2nd law The total P.Ds in a circuit adds up to give the total E.M.F in a circuit.
Voltage Voltage (V) or Potential Difference (p.d.) is a measure of the Energy transferred or Work done per Charge Carrier between two points.
V= Voltage is the Energy, E per Charge; Q. Voltage is measured in Volts (V), which is defined as one Joule per Coulomb. Voltage can be defined in base units as Kgm2s-3A-1.
E.M.F E.M.F or Electromotive Force is the creation of Electrical Energy from other forms of energy. E.M.F = Energy Giver
P.D = Energy Taker
=
,W= Q
E.M.F is measured in Volts (V).
36 | P a g e
Power Power (P) is the rate of Energy transfer. It is measured in watts (W), where one watt is defined as one Joule per Second. Hence watts can be expressed in base units as Kgm2s-3
=
or P=IV
Measuring Voltage and Current Voltage
Use a voltmeter. Voltmeters typically have a very high or infinite resistance. The voltmeter must be connected in parallel.
Current
Use an ammeter. Ammeters have very low resistance so that they do not affect the current that they’re measuring. The ammeter must be connected in series.
Short Circuits Current will always choose the path with least resistance. This circuit will not light because there is a path available with less resistance (i.e. without a bulb) for Mr. Coulomb. This obviously means that the current would choose to take that path instead, which means the bulb won’t light
Energy Transfer To calculate energy transfer: Energy Transferred (J) = Current (A) x Voltage (V) x Time (s) E=IxVxt
Current:
The rate of flow of charge/electrons Is equivalent to one coulomb per second
Voltage:
Energy transferred per unit charge passed Joule per coulomb Is the force that pushes the current around the circuit
37 | P a g e
Movement of Electrons (Drift Velocity) The drift velocity is a velocity that is superimposed on the random motion of the charge carrier, The increase in velocity causes the charge carriers to collide more, therefore cause and equal and opposite force which by Newton’s First law, gives a rise to current. For a Conductor, this current is given by:
I= n x A x V x q I= Current A= X-Sectional area of conductor N= Number of charge carriers (free electrons) per m3 Q= Charge of each carrier V= drift velocity of charge carriers
Conduction Processes of Metal Metals have atomic lattices that vibrate in their fixed positions, these atoms will have electrons bound to them and there will also be free electrons which vibrate around them. When Voltage is applied it will make the free electrons drift towards the positive terminal. This increase in acceleration will make them collide into the atoms. This will limit the flow of electrons (Current) and as they collide they transfer they’re kinetic energy into the atoms and cause them to vibrate more. An increase in voltage will lead to an increase in Current and therefore they’ll be more collisions and make the material appear more resistive.
Conduction Processes of Semi-Conductors An increase in current speeds up the flow of electrons. They will collide with atoms. This will transfer more kinetic energy to the atoms. The increased kinetic energy will cause the atoms to vibrate more to the point where they expel electrons. This will increase the N number of free electrons and therefore cause it to be more conductive.
Ohm’s Law To calculate resistance: Voltage (V) = Current (A) x Resistance (Ω) V = IR Ohm’s Law: The current that flows through a conductor is directly proportional to the potential difference (voltage) across its ends, provided its temperature remains the same. Basically, current flowing through a wire/resistor is directly proportional to the voltage. It also means that resistance stays constant. However, this is not the case for a metal filament bulb. Resistance of the bulb increases because temperature increases. When temperature increases, the positive atoms vibrate more vigorously, impeding the flow of electrons. You get a curve (left picture).
38 | P a g e
Resistors and Resistance The Resistance (R) of an electrical component is a measure of its opposition to an electric current flowing in it. Resistance is measured in Ohms ( ). According to Ohm's Law, voltage is the product of current and resistance. Therefore Ohms can be expressed in base units as Kgm2s-3A-2. Everything has Resistance, because everything has some opposition to the flow of Electric Charge. Components whose sole purpose is to provide a Resistance of a certain value are called Resistors. Resistors are used in circuits to control the sizes of currents and voltages. Without one, the voltage across a bulb may cause too large a current to flow through and cause the bulb to blow. An extra amount of energy is needed to push charges through the resistance, and this can cause a rise in temperature as the energy may be converted to heat.
There are two types: Fixed resistors – They have a fixed amount of resistance. Variable resistors – Resistance can be varied to increase/decrease the current. It is used in the remote control to alter the volume of the TV, and also used to control the speed of a motor.
Resistors in Series When Resistors are connected in Series, the total Resistance across them will be equal to the sum of each Resistor value. The total voltage will be equal to the sum of the voltages across each Resistor. This rule will also apply for other components.
Rtotal = R1+R2+R3+ …. Resistors in Parallel When Resistors are connected in Parallel, the reciprocal of the total resistance will be equal the sum of the reciprocals of each Resistor Resistance. The total voltage dropped will be the same as the voltages dropped across all the individual Resistors.
=
+
+
+…
Power Dissipation in a Resistor Power (P) transferred in an electrical component is given by:
=
or P=IV
The unit for power are Watts (W) = J/s When a charge flows through a resistor, work is done on the resistor. It is sometimes convenient to express the power transferred in the resistor in terms of its resistance (R) and the Current (I) in it.
39 | P a g e
R = , or V = IR, so: P=IV = I x (IR) = I2R We Can similarly show, by substituting I = , that:
P=
,
Power is dissipated in a resistor, particularly if that resistor is in the form of the filament of a lamp or the element of an iron or kettle. Dissipated means ‘Scattered’. The electrical energy transferred in the resistors increases the potential energy of the random kinetic energy of the atoms of the material of the resistor (the Internal Energy of the Atoms).
Resistivity Resistance is a Sample Constant, so is specific to individual components. However, there is a Material Constant that can be used to find the Resistance of any component of a specific material. This is Resistivity. Together with the length and cross-sectional area of a sample, you can calculate its resistance. As temperature increases the resistance increases. Resistance depends on temperature. For metals, the higher the temperature, the greater the lattice vibrations and so the harder it is for the electrons to get through.
A
R= , R=
I = 0.25A
2l
= 34 V V = 8.5 v
Adding resistors in series. The result shows that resistance is directly proportional to length. R A long wire is like lots of identical resistors in series.
L
�
R = đ??ź, I = 0.5A
R=
= 16 Ί
V V = 8v
40 | P a g e
�
I = 0.79A 2A
R = đ??ź, R=
7
7
The Resistance has decreased as the cross sectional area of the resistor is doubled. The bigger the cross sectional area, the smaller the resistance.
= 11.2 Ί
V V = 7.9 v
Resistivity =
=
=
Resistivity is given the symbol Ď and is measured in Ohm Meters (Ίm, or Kgm3s-3A-2 in base units). R
L, R
is the Resistivity of the material, it is temperature dependant.
Conservation of Energy in Circuits
Internal Resistance If you took a 12V battery and connected a voltmeter across it, you would find that the potential difference is less than 12V. This is due to internal resistance in the cells of the battery. As electrons pass through the cell, energy is transferred to them from the chemical energy stored in the cell. This process and the chemicals themselves provide resistance and this is known as internal resistance. The potential difference measured from the voltmeter is equal to the EMF of the battery (12V) minus the volts lost due to the internal resistance (Ir). Since V = IR from Ohm's law the potential difference of a cell or other power supply can be calculated using this formula:
V = - Ir, Where V is the 'external voltage' (reading when a voltmeter is put across the power source), is the EMF of the power source, I is the current and Ir is the internal resistance of the power source. Alternatively the Current can be calculated by dividing both sides by I to give:
I=
41 | P a g e
Measuring Internal Resistance To measure internal resistance you should first refer back to the above equation, V = - Ir Rearranged as V = -Ir + to give an equation similar to the equation of a straight line (y = mx + c). This is how internal resistance is measured, by applying a 'load resistance' (a resistor across the power source) and varying it's resistance with a Rheostat to get a range of values for V and I which can then be measured by using a voltmeter and ammeter.
When plotted against one another a straight line is given with an intercept of the EMF and gradient of -r, the internal resistance.
The Potential Divider Potential dividers, as the name suggests, divide potential. Electrical potential in fact using resistors like in the circuit below:
The two voltages across the two resistors are related by a simple relationship:
= This is as a result of Ohm's law. Alternatively a more useful and altogether powerful equation for calculating the output of the potential divider is:
Vout = Vin x 42 | P a g e
Example: A potential divider made from two resistors of 100 and 200 is supplied with a voltage of 12V. What are the potential differences across the resistors? This question involves using the relationship between the ratio of voltages and resistances. Since the resistances are twice as much as each other so are potential differences, hence the potential difference across the 200 Ohm resistor is 8V and the 100 Ohm resistor is 4V. You could also use the full equation with R1 as 100 and R2 as 200:
Other Circuit components Thermistors Thermistors are used as temperature sensors, for example, in fire alarms. It is made from semiconducting material such as silicon or germanium. At low temperatures, the resistance of a thermistor is high, and little current can flow through them. At high temperatures, the resistance of a thermistor is low, and more current can flow through them.
Light-Dependent Resistors (LDR) LDRs (light-dependent resistors) are used to detect light levels, for example, in automatic security lights, photographic equipment, automatic lighting controls and burglar alarms. In the dark and at low light levels, the resistance of an LDR is high, and little current can flow through it. In bright light, the resistance of an LDR is low, and more current can flow through it.
Diodes Diodes are resistors that direct the flow of current to one direction only. Current can only flow through one direction due to a part of the diode with low resistance and cannot flow the opposite way due to the high resistance at the other end of the diode. Diodes are used in rectifier circuits that convert alternating current to direct current. It can also make logic gates (something in the Cambridge syllabus and thank GOD it is not Edexcel). All these resistors can be investigated by sticking them into a circuit and adjusting the voltage, then comparing it with the current and then plotting a graph.
43 | P a g e
A.C and D.C Alternating Current
The flow of electricity is constantly changing direction.
Mains electricity supply provides alternating current.
Direct Current
The flow of electricity is in one direction.
Cells and batteries provide this.
Conductors and Insulators
Conductors allow current to flow easily through the circuit. These are usually metals, where charge is carried by the free electrons that are able to move throughout the whole of the metal.
Insulators are poor conductors. These are things like plastic and fabric.
44 | P a g e
Circuit Symbols Open Switch
Closed Switch Lamp Cell Battery Voltmeter Resistor Fuse Ammeter Variable resistor Thermistor Light dependent resistor (LDR)
45 | P a g e