Kirchoff

Experiment 1

Kirchoff's Current and Voltage Laws Objective: <

To study the relation between current and voltage in DC circuits, and to observe resistance, current, and voltage relationships in series and parallel combinations.

Equipment: < < < < <

Digital multimeters, 2 DC power supply, IP18, 0-15 V, 2 Resistors, 100 S, 1000 S, 2200 S, 3300 S, 4700 S Bread boards Bread board leads

Physical Principles: Ohm's Law For many materials the current resulting when a voltage is applied is directly proportional to the voltage. The proportionality constant is defined by R

V I

(1)

where R is called the resistance and is measured in ohms.

Resistors in Series The effective resistance of the three resistors in figure 1 connected in series is equal to the sum of the resistances of each resistor.

Req R1 R2 R3

Resistors in Parallel

(2)

Figure 1 Resistors in series.

R1 The effective resistance of three resistors connected in parallel (see figure 2) is given by the following formula.

1 1 1 1 Req R1 R2 R3

R2 R3

(3) Figure 2 Resistors in parallel.

Kirchoff's Current Law

I3

I1

According to this law, the sum of the currents leaving a node is zero. A node is a point where more than two conducting paths connect.

I2

So, in the case of figure 3 it can be said that I1 I2 I3 0

(4) Figure 3 Diagram of a node.

Kirchoff's Voltage Law

V1 +

The sum of all the voltage drops within a loop always adds up to zero.

-

+

-

-

+

V2

According to the figure 4, the following equation can be written.

V1 V2 V3 0

V3

(5) Figure 4 Diagram of a closed loop.

Procedure: Part 1 Connect the three resistors with values of about 2200 S, 3300 S, and 4700 S in series as shown in figure 2. Measure and record the values of R1, R2 , R3, and Req. Find the percent error between the measured value of Req and the value predicted by equation (2).

Part 2 Connect the IP18 across the three resistors in series with an ammeter as shown in the figure 5 below. Set the voltage to about 15 volts. Read the voltage and the current from the digital meter displays. Disconnect the voltmeter from its original position and measure and record the voltages VDC, VCB, VBA, and VCA. Compare these values with the products of the current and the corresponding resistance values, as shown below.

VD C I@RDC VC B I@RC B VB A I@RBA

4700 S A

VC A I@(RC B RB A)

Figure 5 Voltage across series resistors Part 3 Measure the resistance of the parallel combination of two resistors R1 = 2200 S and R2 = 3300 S. See figure 3 for assistance. Compare the result with the value of Req obtained from equation 3.

Part 4 Connect the IP18 to the parallel combination of the resistors R1, R2 as shown in figure 6. Set the IP18 voltage to approximately 15 volts. Connect the meters in such a way that you can measure the supply voltage and the currents labeled as I, I1 and I2. Compare these values for the currents with I6

I1

V R1

9 I1 V

I2

9 I2

+

V R2

R1

-

R2

I I1 I2

Part 5

Figure 6 Current through parallel resistors

Connect the IP18 in series with a 1000 S resistor, a 100 S resistor and an ammeter as shown in figure 7. Set the IP 18 voltage to about 15 volts. Measure the voltages VCB and VCA. Why is there a difference in these readings?

IP 18 1000 S

C

100 S

V A

B

A

Figure 7 Voltage and current measurements Part 6 Choose three resistors with values about 200 S, 300 S and 500 S. Since these values are not exact, measure the value of each resistor using the meters provided. Build the circuit in figure 8, and then record the values of V1, V2 and I1, I2, I3 and compare with the theoretical values that you can find by using Ohmâ&#x20AC;&#x2122;s Law and Kirchoffâ&#x20AC;&#x2122;s Laws. You may use the Mathcad example given as a template to solve for the theoretical values.

V1 = 10 V +

V2 = 5 V

-

+

+

+ I1

-

-

I2

I3 -

+ -

Figure 8 A simple current network

Mathcad Sample Document

R1

200

R2

300

R3

500

V1

10

V2

5

Now, initial guesses for the currents must be entered I1

1

I2

1

Given I1

I2

I3

1

Note: You must type in the word "Given" exactly as it is!

I3 0

R1. I1

R2. I2

10 0

R2. I2

R3. I3

5 0

The equal sign in these equations is obtained by holding down on the CNTRL key while typing =

0.031 Find( I1 , I2 , I3 ) = 0.013 0.018

Type the regular equal sign in this equation to evaluate your answers.

Recording data Part 1 Measured Values

Calculated Values

R1 R2 R3 Rtot Part 2 Measured Values

Calculated Values

VDC VCB VBA VCA Part 3 Measured Values

Calculated Values

R1 R2 Rtot Part 4 Measured Values I1 I2 I

Calculated Values

Part 5 What is the reason that VCB is slightly different from VCA? Part 6 Measured Values I1 I2 I3

Calculated Values