Physics 260 Calculus Physics II: E&M
Grist
Laboratory Exercise: Kirchhoff’s Rules
Object
Through experiment you will determine if the currents and voltage drops in a two loop circuit
obey Kirchhoff’s rules.
Introduction
A two loop circuit is a circuit that has two distinct, yet interconnected, current paths through
which current may flow. You will be measuring the currents and voltage drops in a two loop
circuit with multiple resistors and emf sources and comparing your measurements to calculated
values.
What are Kirchhoff’s rules?
1) The Junction Rule. This states that when you have a point where two or more wires connect
(a junction) the sum of the currents going in to the junction must be equal to the sum of the
currents leaving the junction. This makes sense if you consider the law of conservation of charge
– you can’t suddenly gain (or lose) charges from nowhere just by entering or exiting a junction.
2) The Loop Rule. This states that the sum of all the voltage drops and emf sources around a
loop must equal zero. This make sense if you consider that the emf (voltage) provided is
distributed over the resistances in the loop – you can’t ‘magically’ have voltage that isn’t
provided by some emf source.
Kirchhoff’s Rules 1
Physics 260 Calculus Physics II: E&M
Grist
The Two Loop Circuit
I1
I2
R2
R5
R3
I3 loop 2
loop 1
E1
R1
E2
R4
Figure 1
By applying Kirchhoff’s rules to the two loop circuit in Figure 1, we get the following equations:
(1)
(2)
E1  V2  V3  V1  0
E1  R2 I1  R3 I 3  R1 I1  0
 E2  V4  V3  V2  0
[Loop 1]
[Loop 2]
 E2  R4 I 2  R3 I 3  R5 I 2  0
(3) I 3  I 2  I1
[Junction]
If we know the resistances and the emf values, then we have three equations with three
unknown values (I1, I2, and I3). We can now use any one of several method of solving
simultaneous linear equations and find the unknowns.
Procedure
1. Arrange the circuit shown in Figure 1 using first set of resistors.
2. Adjust the two power supplies: E1 to 10 V dc and E2 to 5 V dc.
3. Using the ammeter function on the multimeter measure the current I1 through R2 and
record on the report sheet.
4. Now measure the current I2 through R5 and record on the report sheet.
5. Measure the current I3 through R3 and record on the report sheet.
6. Also measure the currents through R1 and R4 and record on the report sheet.
7. Now using the voltage function on the multimeter measure and record the voltage drop
across each resistor.
8. Now using the ohmmeter function on the multimeter carefully remove, measure and
record the resistance of each resistor.
Now repeat with the second set of resistors
Kirchhoff’s Rules 2
Physics 260 Calculus Physics II: E&M
Grist
Comparison and Analysis
(You can attach extra pages to show you calculations if necessary)
1) Using equations (1), (2), and (3) in the RnIn form, and the measured values of the power
supplies and the resistors, solve for the three currents. Show your work. This is a great place to
use linear equations methods (matricies). Compare your calculated values to the measured
values of the currents. Do the measured and calculated values agree closely enough to validate
Kirchhoff’s rules (<10%)?
2) Using your measured values for the currents does I 3  I 2  I1 within reason enough to
validate Kirchhoff’s junction rule (<10%)? Show and comment.
3) Using your measured values for R, E and I do the loop equations (1) and (2) agree closely
enough to validate Kirchhoff’s loop rule? Show and comment.
4) Why are the voltages with the two sets of resistors the same, while the currents are different?
Kirchhoff’s Rules 3
Physics 260 Calculus Physics II: E&M
Grist
Name_____________________________
DATA SHEET
Resistor Set 1
Measured
E1
E2
I1
I2
I3
IR1
IR4
ΔV1
ΔV2
ΔV3
ΔV4
ΔV5
R1
R2
R3
R4
R5
Calculated
Resistor Set 2
Measured
Calculated
E1
E2
I1
I2
I3
IR1
IR4
ΔV1
ΔV2
ΔV3
ΔV4
ΔV5
R1
R2
R3
R4
R5
Kirchhoff’s Rules 4