College Physics Lab
PH 144
Kirchoff's Rules and Equivalent Resistance
Purpose: To verify Kirchoff's rules. To verify the rules for combining resistors which are in
series and in parallel.
Discussion: Kirchoff's loop rule states that the algebraic sum of the changes in voltage around
any closed loop in an electric circuit is zero. You are going to verify the loop rule by measuring
the voltage change across each element in each loop (using a voltmeter). As you progress around
a loop make sure that you note whether the voltage change is positive or negative. The sum of all
these voltage changes should be zero, unfortunately you will probably not get exactly zero. How
close to zero is acceptable? Define V+ as the sum of all the positive voltage changes and V- as
the sum of all the negative voltage changes in a particular loop. We can reword the loop rule to
say that V+ = |V-|. We can now check the loop rule by calculating the percentage difference
between V+ and |V-|,
% difference = X 100
As you make the voltage measurements keep in mind that the voltmeter is placed in parallel with
the circuit element and that it should have a relatively large internal resistance so as to allow very
little current to be diverted through it.
Kirchoff's junction rule states that the sum of the electric currents flowing into any junction in an
electric circuit equals the sum of the currents flowing out of the junction. You will verify the
junction rule by measuring the current in each path leading into or out of each junction (using an
ammeter). Define Iin as the sum of all the currents flowing into and Iout as the sum of all the
currents flowing out of a particular junction. The junction rule states that Iin = Iout, and the
percentage difference is,
% difference = X 100
As you make the current measurements keep in mind that the ammeter is inserted into the loop in
series and that it should have a relatively low internal resistance so as to not to significantly
reduce the current in the loop.
A note about safety: You will be using a voltage of around 2 V to produce a current of 0-100 ma
(1 ma = 1 milliampere = 0.001 Ampere). Always start with a low voltage and a large resistance.
Increase the voltage slowly and decrease the resistance in small steps. As long as you observe
these simple precautions, this experiment should be safe for both you and the equipment.
Procedure:
1. Make a one-loop circuit with a battery and one resistor. Measure the voltage changes across
the battery and the resistor. Check the loop rule as described above. Verify that there is no
measurable voltage change across the wires, because they have relatively little resistance.
2. There are no real junctions in this circuit. Verify that the current is the same throughout the
loop by inserting the ammeter at different points along the loop. You will need an extra wire to
accomplish this.
3. Use the measured voltage across the resistor and the measured current flowing through the
resistor to calculate the resistance. It will not necessarily be exactly the same as the resistance
marked on the resistor!
4. Make a one-loop circuit with a battery and two resistors. The two resistors are connected in
series. Measure the voltage changes across the battery and across each resistor. Check the loop
rule as described above.
5. Again, there are no real junctions in this circuit. Verify that the current is the same throughout
the loop. You will have to put the ammeter between the power supply and the first resistor,
between the two resistors, and between the second resistor and the power supply.
6. Use the measured voltage across each resistor and the measured current flowing through each
resistor to calculate the resistance of each resistor.
7. Measure the total voltage across the power supply. Calculate the equivalent resistance of the
two resistors when they are connected in series. Is this equivalent resistance the same as the sum
of the two resistances calculated in step 6?
8. Make a two-loop circuit with a battery and two resistors. The two resistors are connected in
parallel. Measure the voltage changes across the battery and across each resistor. Check the loop
rule for each loop as described above. Notice that in going around the loop with the two resistors
you will have to go through one of the resistors in the direction opposite to the current.
9. There are two junctions in this circuit. Check the junction rule for each junction as described
above.
10. Use the measured voltage across each resistor and the measured current flowing through each
resistor to calculate the resistance of each resistor.
11. Measure the total current flowing through both resistors. Calculate the equivalent resistance
of the two resistors when they are connected in parallel. Is the reciprocal of this equivalent
resistance equal to the sum of the reciprocals of the resistances calculated in step 10? Evaluate
the % difference to support your claim.