This question is based on a practical method to determine the resistivity of a metal wire, Y.
The diameter of wire Y is measured using a micrometer screw gauge. The main scale has a resolution of 0.50 mm0.50\text{ mm}0.50 mm. The edge of the thimble is aligned exactly with the 0.50 mm0.50\text{ mm}0.50 mm mark on the main scale, and the 000 division on the thimble scale is aligned exactly with the horizontal datum line. State the diameter ddd of wire Y in mm.
In an experiment to find the resistance per unit length of wire Y, a series resistor of resistance 2.2 Ω2.2\ \Omega2.2 Ω is connected in series with a cell, a switch, and wire Y.
Show that the resistance RRR of the wire between the voltmeter clips is approximately 1.0 Ω1.0\ \Omega1.0 Ω.
The student determines the resistance RRR for several different lengths LLL of wire Y and plots a graph of RRR against LLL. The gradient of this graph (the resistance per metre of wire Y) is 2.42 Ω m−12.42\ \Omega\text{ m}^{-1}2.42 Ω m−1.
Table 1 shows the manufacturer's values for the resistance per metre of four different metals at various wire diameters ddd.
| Diameter ddd / mm | Copper / Ω m−1\Omega\text{ m}^{-1}Ω m−1 | Tungsten / Ω m−1\Omega\text{ m}^{-1}Ω m−1 | Constantan / Ω m−1\Omega\text{ m}^{-1}Ω m−1 | Nichrome / Ω m−1\Omega\text{ m}^{-1}Ω m−1 |
|---|---|---|---|---|
| 0.250.250.25 | 0.3460.3460.346 | 1.141.141.14 | 9.989.989.98 | 22.422.422.4 |
| 0.500.500.50 | 0.08660.08660.0866 | 0.2850.2850.285 | 2.502.502.50 | 5.605.605.60 |
| 0.800.800.80 | 0.03380.03380.0338 | 0.1110.1110.111 | 0.9750.9750.975 | 2.192.192.19 |
(i) Identify the metal used for wire Y. (ii) Determine the resistivity ρ\rhoρ of this metal. State an appropriate SI unit for your answer.
The student adds error bars for RRR and LLL to each plotted point. She estimates that:
Compare her error bars for the point at L=100 mmL = 100\text{ mm}L=100 mm (where R=0.25 ΩR = 0.25\ \OmegaR=0.25 Ω) with her error bars for the point at L=400 mmL = 400\text{ mm}L=400 mm (where R=1.00 ΩR = 1.00\ \OmegaR=1.00 Ω).
37 exam-style questions on AQA A Level Physics Current electricity, covering Basics of electricity, Current-voltage characteristics, Resistivity, Circuits, Potential divider, and Electromotive force and internal resistance. Each one has a worked solution and a mark scheme showing where the marks go.