The method and the results are on the kirchhoff's rules lab. Do the analysis yourself first, then check the answers below.
Quick answer: In a DC circuit, a wire's resistance is R = ρL/A, series resistors add, and parallel resistors share the same voltage. These answers go with the AP Physics 2 lab on kirchhoff's rules: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The sample data give a straight line through the origin with gradient close to 8.0 Ω/m. The answers below show how to turn the gradient into a resistivity and how to judge its uncertainty.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 11
Question 1 Resistance values
R = V/I = 1.12 / 0.235 = 4.77 Ω. R increases steadily with L: from 1.60 Ω at 0.20 m to 8.00 Ω at 1.00 m.
Question 2 Graph
The graph is a straight line, so R is directly proportional to L. A zero length of wire has zero resistance, so the line should pass through the origin.
Question 3 Gradient
Gradient = (8.00 − 1.60) / (1.00 − 0.20) = 6.40 / 0.80 = 8.0 Ω/m.
Question 4 Resistivity
R/L = ρ/A, so ρ = gradient × A = 8.0 × 6.2 × 10⁻⁸ = 4.9 × 10⁻⁷ Ω·m. This agrees with the accepted value.
Question 5 Uncertainty in the area
The percentage uncertainty in d is 0.01 / 0.28 = 3.6 %. Since A depends on d², the uncertainty in A is 2 × 3.6 % = 7.1 %. The resistivity has about the same uncertainty: 4.9 × 10⁻⁷ ± 0.35 × 10⁻⁷, so ρ = (4.9 ± 0.4) × 10⁻⁷ Ω·m.
Question 6 Why open the switch
Current heats the wire, and a hotter metal has a higher resistivity. Opening the switch keeps the temperature constant. If the wire heated, R would read too high at the longer lengths and the graph would curve upwards.
Question 7 Improving the method
A positive intercept comes from contact resistance at the clips, or a zero error in the length. Improve it by measuring the voltage directly between the clips (as in this set-up) and using sharp, clean clip contacts.
