Quick answer: In a DC circuit, a wire's resistance is R = ρL/A, series resistors add, and parallel resistors share the same voltage. This AP Physics 2 lab on kirchhoff's rules gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How does the resistance of a metal wire depend on its length, and can a straight-line graph give the resistivity of the metal? In this lab you collect voltage and current data, plot resistance against length and use the gradient to find a property of the material itself.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 11
Aim
Measure the resistivity of a constantan wire by finding how its resistance depends on its length.
Equipment
- constantan wire, about 1.2 m, diameter near 0.28 mm
- metre rule and tape
- power supply set to 3 V d.c. (or two 1.5 V cells) with a switch
- ammeter (0–1 A) and voltmeter (0–3 V)
- two crocodile clips and connecting leads
- micrometer screw gauge
Safety
The wire warms up when current flows. Keep the switch open except when taking a reading, and do not touch the wire while the current is on.
Method
- Measure the diameter of the wire at three places with the micrometer. Calculate the mean and the area A = π(d/2)².
- Tape the wire straight along the metre rule and build the circuit shown.
- Place the sliding clip at L = 0.20 m from the fixed clip. Close the switch, read V and I at once, then open the switch.
- Repeat for L = 0.40, 0.60, 0.80 and 1.00 m.
- Calculate R = V/I for each length.
Results
Sample data, mean diameter 0.28 mm, A = 6.2 × 10⁻⁸ m²:
| Length L (m) | Voltage V (V) | Current I (A) | R = V/I (Ω) |
|---|---|---|---|
| 0.20 | 0.40 | 0.250 | 1.60 |
| 0.40 | 0.78 | 0.245 | 3.18 |
| 0.60 | 1.12 | 0.235 | 4.77 |
| 0.80 | 1.42 | 0.225 | 6.31 |
| 1.00 | 1.72 | 0.215 | 8.00 |
Analysis questions
Question 1 Resistance values
Check the table. Calculate R for L = 0.60 m and describe the trend of R with L.
Question 2 Graph
Plot R (y-axis) against L (x-axis), draw the best-fit line and state its shape. Explain why the line should pass through the origin.
Question 3 Gradient
Calculate the gradient of the line using the first and last points of the table. Give its unit.
Question 4 Resistivity
Use the gradient and the area A to calculate the resistivity of the wire. The accepted value for constantan is about 4.9 × 10⁻⁷ Ω·m. Comment.
Question 5 Uncertainty in the area
The micrometer reads to ±0.01 mm on a diameter of 0.28 mm. Calculate the percentage uncertainty in A and the resulting uncertainty in ρ.
Question 6 Why open the switch
Explain why the switch is opened between readings, and what would happen to the readings if the wire heated up.
Question 7 Improving the method
A student finds that the best-fit line has a small positive intercept on the R axis. Suggest a cause and one improvement.
