Stevens High School AP Physics II Laboratory Manual

Purpose: The purpose of this lab is to give you some circuit construction and multimeter experience while investigating Ohm’s Law, Kirchhoff’s Rules, and the formulas for equivalent resistance. You will examine the impact of wire resistance and so-called contact resistance as well. A formal report will be expected.

Concept:Ohm’s Law states that the potential difference, V, across a resistor is directly proportional to the current, I, through it. The constant of proportionality is the resistance, R:

Materials which fit this relationship are considered ‘ohmic’. Nonohmic materials have a resistance which varies with the current passing through them. In fact, all materials can be classified as nonohmic if enough current is forced through them as they will heat up and scatter electrons more intensely and frequently. However, within reasonable ranges, many materials are ohmic.

Kirchhoff’s Rules are a restatement of the Law of Conservation of Charge and the Law of Conservation of Energy, two of the central pillars of physics. The Junction Rule states that the sum of electric currents entering a junction is equal to the sum of electric currents leaving that junction:

The Loop Rule states that the sum of all potential differences in any closed, non-intersecting path through a circuit must be zero:

In this laboratory, you will be using a digital power supply which can be seen as an ideal battery, with no internal resistance. Of course, there are numerous losses within the power supply itself, but for our purposes the output is a user-selectable output emf, .

Materials:

  • (1) Digital power supply. Please be very responsible with these units. They cost upwards of $1500/unit.
  • (1) Multimeter
  • (5) Resistors – any value is acceptable.
  • (16-20) Alligator leads. One pair may have banana plug connections on one end.
  • Recording instrument and substrate.

Procedure:

1)Build the circuit below.

Figure 1: Schematic of circuit for lab. I have indicated a suggested layout with wires that will easily allow you to measure the electric current at each ammeter location (A1, A2, etc). The resistors are shown as rectangles; this is one accepted circuit schematic symbol for them and it matches the shape you’ll have in the lab. I have indicated voltmeter readings at four locations, including around the power supply which I have indicated as a battery. I did not show the two remaining voltmeter locations to avoid clutter.

2)Develop a data table like the one shown below.

3)Turn on the power supply (small green button on lower left), and adjust the voltage to a reasonable value (1.0 to 4.0 volts).

  1. Press ‘V-Set’, and type “1.00” or your desired voltage, then press enter. In a couple of seconds, the display will stop flashing and read ‘0.00 V, 0.000 A’.
  2. Press ‘I-Set’, and type “1.00”, then press enter. This will limit the current in your circuit to 1.0 A.
  3. Press the ‘Output on/off’ button. It will illuminate when current is flowing through your circuit. You will notice that the display will also give you a reading for voltage and current. These are the value of  and A1 in the schematic above.

4)Measure each potential difference (voltage) V1 – V5 with your multimeter. Remember,  is read off of the power supply display. Ensure that you are using the multimeter correctly. It must be in parallel with the element you wish to measure the voltage across and be set to measure DC volts.

Element / V, Potential Difference [V] / I, Electric Current [A] / Rmeas, Resistance []
R1
R2
R3
R4
R5
 / n/a

Table 1: Raw data from the lab.

5)Measure the current at each of the ammeter locations A2-A5, and record the value in your table. Remember that A1 is read off of the power supply display. Ensure that you are using the multimeter correctly. It must be in serieswith the element you wish to measure the current (or amperage) through and be set to measure DC amps.

6)Measure the resistance of each resistor with the multimeter, Rmeas, and record the value in your table. Do not simply write down the printed value as these are often off by 10% or so.

Data Analysis:

1)Calculate the expected resistance of each resistor, Rcalc, using Ohm’s Law (eq. (1)) and your recorded values of potential difference and current for each resistor and include them in a table like that shown below.

  1. Include a calculation of the percent difference for each resistor.
  2. Give an explanation for any discrepancies you note.

Element / V, Potential Difference [V] / I, Electric Current [A] / Rmeas, Resistance [] / Rcalc= V/I, Resistance [] / Resistance Difference [%]
R1
R2
R3
R4
R5

Table 2: Raw and reduced data from the lab.

2)Check the junction rules (eq. (2)) for this circuit. While there are 4 junction rules, 2 are redundant. Write out two non-redundant junction rules and use your data to check if they are accurate. For instance, in the circuit above, it is expected that I1 = I2 + I5 (I am assuming that the current is upward on the left side of the circuit and downward in the other portions).

So, if my values of I1, I2, and I5 were 1.34 A, 0.65 A, and 0.78 A, respectively, I would write:

, so

The experiment suggests that . This is within 6.3% of the expected result.

3)Write out three loop rules (eq. (3)) (the loops you should check are below), and check if they are accurate. Loop 1 in the circuit above, with currents as I have already explained, we yieldVloop1 = 0. Thus,  - I2R2– I3R3- I1R1 = 0.

So, if the value of I1, I2, and I3 were 1.34 A, 0.65 A, and 0.31 A, respectively, I would write:

, so

Then, substitute in your values for each variable as shown in the previous step and calculate a percent difference for each loop.

4)Explain any discrepancies in the junction rules.

5)Explain any discrepancies in the loop rules.

6)(+5 bonus). Write out an equation for the overall equivalent resistance of the circuit. Assume each wire (labeled W1 – W14) has a resistance Rw. Your equation will start something like this:

Then, use your experimental values of current, voltage, and resistance to calculate the average wire resistance. Finally, explain how the wire resistances account for your answer to part 5.

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