Phy132/222 Experiment
Kirchhoff’s Rules
(revised 7/2/08T)
Name: _______________________________
Date: _____________
Lab Partners: ________________________________________
Introduction: So far you have explored series and parallel combinations of resistors with one battery. To
determine the behavior of more complicated circuits you would reduce them to equivalent circuits. This is
not possible when you have multiple batteries and loops in a circuit. These situations require the application
of Kirchhoff’s Rules summarized below (keep in mind these are not new laws, but applications of the laws of
conservation of energy and conservation of charge to circuits):
1) Junction Rule (Conservation of Charge): The sum of the currents entering a junction equals the sum of
the currents leaving the junction.
I2
I1
I1 = I2 +I3
Junction
I3
2) Loop Rule (Conservation of Energy): The sum of the potential differences in a closed loop is zero.
R1
R2
R3
3.0 V
4.0V
2.0V
V = 9.0V
If you follow the loop clockwise starting at the battery you will gain 9.0 V at the battery and lose 3.0V at R 1,
4.0V at R2, and 2.0V at R3. This follows Conservation of Energy.
V – IR1 – IR2 – IR3 = 0
Or using the voltages from the figure above:
9.0V – 3.0V – 4.0V – 2.0V = 0
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If you follow the loop in the counterclockwise direction energy is still conserved. Now you are losing energy
crossing the battery from the positive to the negative terminal (0V – 9.0V = - 9.0V) and you gain energy as
you cross each resistor since you are traveling against the direction the current is flowing.
- V + IR3 + IR2 + IR1 = 0
or
- 9.0V + 2.0V + 4.0V + 3.0V = 0
In either direction the result follows from the Conservation of Energy.
Part I: Circuit 1.
Measure the resistance of each of your resistors using your DMM. Set up the circuit in Figure 1 below. Use a
battery for the 6 V voltage source, and the power supply as your 12 V voltage source. Notice that there are
predictions for the directions of the three currents indicated in the diagram. Use these as your own predicted
direction for the current. Measure the current flowing through each branch and the potential difference of
each battery. Keep in mind that your DMM is set up for current to flow into the port marked with an A or
mA, then flow out of the port marked COM. If there is a minus sign on your current measurement, then your
current is flowing into the COM port and out of the A/mA port, in the opposite direction than the prediction
in the circuit diagram. That’s ok. Record the current in your data table with the minus sign. Be sure to have
your instructor check the circuit before you begin.
I3
I1
I2
V1
(6 V)
R1
(470 Ω)
R3
(1000 Ω)
R2
(680 Ω)
V2
(12 V)
Figure 1: Two-Loop Circuit
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Part II: Circuit 2.
Measure the resistance of each of your resistors using your DMM. Set up the circuit in Figure 2 below. Use
the indicated currents as your assumed direction for the current in each branch. Measure the current in each
branch. Remember to pay attention to the sign of each measured current. Be sure to have your instructor
check the circuit before you begin.
I1
I2
I5
I3
R3
(220 Ω)
I4
R4
(330 Ω)
R1
(150 Ω)
V1
(6 V)
R2
(100 Ω)
R5
(680 Ω)
V2
(12 V)
Figure 2: Three-Loop Circuit
Proceed to the Questions section.
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Data
Part I:
Data Table 1: Two-Loop Circuit
R1
Measured
Value
R2
R3
Theoretical
Value
Percent
Error
X
X
X
X
V1
V2
I1
I2
I3
Part II:
Data Table 2: Three-Loop Circuit
R1
Measured
Value
R2
R3
V1
R4
V2
R5
I1
Theoretical
Value
Percent
Error
X
X
X
X
I2
I3
I4
I5
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Questions
1.
How do your theoretical results compare with your experimental results for the Two-Loop Circuit?
2.
For the Two-Loop Circuit, determine the amount of power supplied by the battery and the power
supply. Then calculate the total power lost to all the resistors. Compare these two values. Does this
relationship demonstrate a conservation law? Which one?
3.
In the Three-Loop Circuit, why is there no current indicated between the two connection points on the
bottom wire?
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4. The Three-Loop Circuit will require five equations to determine the five unknown currents in all the
loops. You can calculate this by hand if you are up to the grueling task or you may use Mathematica
to solve the series of equations for you. The following website is useful:
http://www.akiti.ca/Mathfxns.html
Good Luck!
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