Ohm's Law - Adding Resistors in Series and Parallel



Lab #6: Kirchhoff's Laws

Copyright R. Mahoney 2013

Name: _______________

The purpose of this lab is to learn how to use Kirchhoff's voltage loop law and current conservation law to analyze a circuit that by its nature is not easily reducible by the usual rules for adding resistors in series and parallel.

1. Set up the following circuit:

[pic]

You will be told what the nominal values are for R1, R2 and R3. V1 is the voltage from a DC power supply. V2 is the voltage from a lantern battery. You will be told to what value V1 should be set. V2 will be measured under load (current flowing). In general, keep the battery (V2) disconnected when you are not making in-circuit measurements.

2. With the resistors out of the overall circuit (removed one at a time), and using an ohmmeter, measure the resistors' resistances:

R1 = _______ R2 = _______ R3 = _______

3. With current flowing in both loops of the overall circuit, measure the voltages across the DC power supply and the battery:

V1 = _______ V2 = _______

Does V2 drift downward?

4. With current flowing in both loops of the overall circuit, measure the voltage drops across the three resistors:

VR1M = _______ VR2M = _______ VR3M = _______

Carefully observe the polarity of the voltage drop across R2. This will tell you experimentally which way the conventional current through R2 is flowing. Is it up or is it down?

5. We identify the currents flowing through R1, R2 and R3 as

I1, I2 and I3 respectively. Using an ammeter, measure these three currents:

I1M = _______ I2M = _______ I3M = _______

Again, carefully observe the polarity of the measured conventional current I2M. Is it up or is it down?

6. Starting at point A in the overall circuit, use Kirchhoff's voltage loop law to write down the sum of the voltage increases and decreases for the loop that includes R1 and R2. For mathematical reasons, assume that the conventional current I2 is up, regardless of what you found experimentally.

7. Starting at point B in the overall circuit, use Kirchhoff's voltage loop law to write down the sum of the voltage increases and decreases for the loop that includes R2 and R3. For mathematical reasons, assume that the conventional current I2 is up, regardless of what you found experimentally.

8. Draw the directions of the conventional currents I1, I2 and I3 on the schematic on the first page of this lab, as you used them in steps 6 and 7. Using Kirchhoff's current conservation law, write down how the three currents are related.

9. Using the simultaneous equations method shown in class, determine what the theoretical values of the three currents should be. Show your work on the backside of this lab.

I1T = _______ I2T = _______ I3T = _______

10. Calculate the % errors between the measured and theoretical currents for all three currents, with the measured currents as true:

% Error, I1 = _______ % Error, I2 = _______ % Error, I3 = _______

11. Using the measured resistances for R1, R2 and R3, and the theoretical currents in step 9, and using Ohm's Law, calculate the theoretical voltage drops across the three resistors:

VR1T = _______ VR2T = _______ VR3T = _______

12. Calculate the % errors between the measured and theoretical voltage drops across all three resistors, with the measured voltage drops as true:

% Error, VR1 = _______ % Error, VR2 = _______ % Error, VR3 = _______

13. State two non-trivial systematic errors for this experiment.

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