ST. LAWRENCE UNIVERSITY
Physics 152
Kirchhoff’s Circuit Laws
Spring 2016
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Introduction
I
This experiment will allow you to examine Kirchhoff’s current
law and voltage law. Short and open circuits will also be examined.
Be sure to set your multimeters to get as much measurement precision
as possible!
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R1
1
I
I
E1
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R2
2
3
R3
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Experiment
1.
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Figure 1
Kirchhoff’s Current Law (the Node Rule)
Kirchhoff’s current law states that the current that enters a junction equals the current that exits the junction: Iin
I2
= Iout. If the current splits as shown at right, then I1 = I2 + I3.
a.
b.
Make a large, neat sketch of the circuit shown in Figure 1 above. Make sure you see
the correlation between this diagram and the circuit board you are using.
I1
I3
Create a table in your report as shown below; note that the ammeter will display currents in units of mA:
R ()
Resistor
Vcalculated = R·I (v)
I (A)
Vmeasured (v)
R1
R2
R3
c.
Before connecting any wires to the circuit, set one multimeter to be used as an ohmmeter and measure
each resistor on your board; write the value of each resistance on your circuit diagram, and in the data table.
d.
Two jumper wires will be used in this experiment to complete the circuit. Connect jumper wire J2
on the right side of the circuit as shown below; this jumper will be in place for the first two
experiments. If you do the optional project (step 6a), this jumper wire will be removed.
e.
Connect the ammeter and jumper wire J1 as shown in Figure 2 below:
R2
R1
A
A
R1
J1
E1
R3
Figure 2 +
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E1
R2
J1
R1
A
J1
J2
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R2
J2
R3
Figure 3
J2
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E1
R3
Figure 4
f.
Connect the DC power supply to your circuit board, set the voltage of E1 to 15.0 volts (as measured on the
voltmeter connected across the circuit board terminals), then measure and record I1, the current through R1
(be sure that the ammeter is adjusted to display with as much precision as possible). Move the ammeter and
jumper wire J1 to the positions shown in Figures 3 and 4 to measure I2, and I3, respectively. The jumper
wire ensures that the entire circuit is powered at all times.
g.
Kirchhoff’s current law states that the total current flowing into a junction is equal to the total current
flowing out of the junction (Iin = Iout). Check your measurements to see if I1 = I2 + I3.
SLU Physics
Revised: 1/7/2016
Kirchhoff’s Circuit Laws
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Department of Physics
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ST. LAWRENCE UNIVERSITY
2.
Physics 152
Kirchhoff’s Voltage Law (the Loop Rule)
Kirchhoff’s voltage law states that the sum of the voltages in each loop of the circuit will be zero:

V  0
around
loop
b.
c.
d.
{
a.
The following sign conventions are used as you move through circuit elements around a loop: the voltage is
negative when following in the direction of current through a resistor; the voltage is positive when
following in the direction of current through a source of Emf.
4.2 V
Measure the voltage across each resistor. Record the measured voltage in your data table,
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and on your circuit sketch; use a curly bracket on the circuit sketch to denote the
magnitude and polarity of the voltage, as shown at right. Some things to consider:
i.
It is important that current flows through the entire circuit during your voltage measurements.
Which configuration of J1 and the ammeter (Figure 2, 3, or 4) should you use? Does it matter?
ii.
You don’t need to switch the position of J1 and the
ammeter for each voltage measurement!
The figure at right shows the three loops you will follow for your
circuit. Identify which resistors are contained in each loop. Is the
voltage source included in each loop?
Loop 1
Loop 3
Moving clockwise around the left loop (“Loop 1”) of your circuit
diagram, determine the sum of the measured voltages and the
voltage source.
Loop 2
Repeat your calculations for the outside loop (“Loop 2”), and then the right loop (“Loop 3”). Are the sums
consistent with Kirchhoff’s voltage law?
THE EFFECTS OF SHORT AND OPEN CIRCUITS ON BULBS IN SERIES AND PARALLEL:
3.
4.
Open circuits:
a.
Connect two light bulbs (of the same wattage) in series (no meters are necessary for this circuit). Draw a
circuit diagram, and turn up the power supply until the built-in meter reads 7.0 V. Unscrew one of the bulbs
and remove it. What happens? Screw this bulb back in, then unscrew the other. Use your circuit diagram to
briefly explain what you observed and why it happened (represent the bulb that was unscrewed by omitting
it from the diagram and leaving a gap in its place).
b.
Turn off the DC power supply using the power button, leaving the voltage set to 7.0 V. Connect the two
bulbs in parallel, draw a circuit diagram, and turn on the DC power supply. Repeat the experiment above,
record your observations, and use your circuit diagram to explain your observations. Describe the
appearance of the bulbs at each step, and compare to their appearance when connected in series.
c.
Based upon your observations, explain whether you think the light bulbs in your house are wired in parallel
or series. Which connection (series or parallel) results in brighter bulbs? Why?
A
Short circuits – Bulbs in series:
Important Note: Have your instructor check your circuit before
turning on the DC power supply!
a.
B
Closed Switch
Connect two light bulbs in series, as shown in the circuit diagram (again, no
meters are required). Your instructor will show you how to connect a knife
Open Switch
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Revised: 1/7/2016
Kirchhoff’s Circuit Laws
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Department of Physics
Canton, NY 13617
ST. LAWRENCE UNIVERSITY
Physics 152
switch across one of the bulbs. Make sure the switch is open, turn on the DC power supply (set to 7.0 V),
and observe the results. Close the switch, and record your observations. Use your circuit diagram to briefly
explain what you observed (draw a closed switch!).
5.
Short circuits – Bulbs in parallel:
Important Note: This experiment cannot be performed when the bulbs are
connected in parallel! Unplug the DC power supply from the AC power before
proceeding!
a.
6.
Unplug the DC power supply's power cord before connecting this circuit. Connect the two bulbs in
parallel, and include a switch to short out one of the bulbs. Draw a circuit diagram, and use it to explain
why we can't turn the DC power supply on without disastrous results.
Optional Project (0.5 point): The Current Law with Two Voltage Sources
a.
Remove the second jumper wire (J2) from your circuit! If you fail to do this, you’ll blow out a fuse!
I1
+
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E1
R1
I2
I
3
R2
R1
R2
E2
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R3
E2
E1
R3
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Note: Remove
second jumper
before connecting
E2
b.
Using the red and black connectors on the power panel, attach a second voltage source E2 as shown above,
and draw a second circuit diagram. The second voltage source is set to 10.0 volts (check the measurement
with your voltmeter). The first voltage source, E1 is still set to 15.0 volts.
c.
Measure the current through each resistor (using the same configurations of the ammeter and J1 as shown in
part 1 above). Compare your measured currents to their expected values. Be sure to observe the polarity of
the resistors (from part 2) when connecting the ammeter.
d.
Use your measured currents to
see if I1 = I2 + I3.
 R 3    E2 R 3 

e. The derivation of the
D

equations for I1, I2, and I3 is
 E1R 3  E2  R1  R 3    where D  R R  R R  R R
tedious, but the solutions for
I2 

1 2
2 3
1 3
the currents with the two
D

sources (defined in the sketch)

 E R  E2 R 1 
are shown at right. Use these
I3  1 2

equations to calculate the
D

expected value of each current.
f.
I1 
E R
1
2
Look carefully at the circuit diagram from step (6a). Now look at your measured and calculated currents.
What’s wrong with this diagram as it is drawn?
Discussion

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
Summarize your numerical results (calculated and measured, and current and voltage sums) from the three
parts of this experiment.
Discuss whether or not your numerical results are consistent with Kirchhoff’s node and loop rules.
Briefly summarize your observations for connecting bulbs in parallel and series.
SLU Physics
Revised: 1/7/2016
Kirchhoff’s Circuit Laws
3 of 3
Department of Physics
Canton, NY 13617