IB Physics HL B.5.12 Resistance and Resistivity Question Bank

Practise IB Physics HL B.5.12 by scaling resistance with wire geometry, deriving resistivity from data, and linking macroscopic results to charge transport.

Exam points

Derive resistance ratios for changed length, diameter, area or material using R = ρL/A.
Interpret resistivity graphs and calculate ρ, radius or length with consistent SI units.
Relate resistivity to carrier density, drift speed and electric field in microscopic models.

[Maximum number: 2]

A cable consisting of many copper wires is used to transfer electrical energy from an alternating current (ac) generator to an electrical load. The copper wires are protected by an insulator.

Figure for Question B.5.12—Resistance and resistivity question 1 — IB Physics HL

The cable consists of 32 copper wires each of length 35 km . Each wire has a resistance of $64 \Omega$ . The cable is connected to the ac generator which has an output power of 110 MW when the peak potential difference is 150 kV . The resistivity of copper is $1.7 \times 10^{-8} \Omega \mathrm{~m}$ .
output power =110 MW

Calculate the radius of each wire.

$\begin{aligned} \text { area }=\frac{1.7 \times 10^{-8} \times 35 \times 10^{3}}{64} \boldsymbol{<}=9.3 \times 10^{-6} \mathrm{~m}^{2} \boldsymbol{\otimes} \text { radius }=\boldsymbol{<} \sqrt{\frac{9.3 \times 10^{-6}}{\pi}}=\boldsymbol{>} 0.00172 \mathrm{~m} \end{aligned}$

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B.5.12—Resistance and resistivity question 1