Resistivity: Practice Questions

A copper wire has a length of \(2.0 \text{ m}\) and a cross-sectional area of \(1.0 \times 10^{-6} \text{ m}^2\). If the resistivity of copper is \(1.7 \times 10^{-8} \Omega \text{ m}\), what is the resistance of the wire?

A heating element is designed to operate at \(230 \text{ V}\) and produce \(2.0 \text{ kW}\) of power. If the heating element is made from a wire with resistivity \(1.0 \times 10^{-6} \Omega \text{ m}\) and a cross-sectional area of \(0.50 \text{ mm}^2\), what length of wire is required?

A wire has a resistance of \(2.5 \text{ k}\Omega\), a length of \(50 \text{ cm}\), and a diameter of \(0.20 \text{ mm}\). What is the resistivity of the material of the wire?

An NTC thermistor and a fixed resistor are connected in series to a constant voltage supply. If the temperature of the thermistor increases, what happens to the total current in the circuit and the potential difference across the fixed resistor?

A metal wire of length \(L\) and cross-sectional area \(A\) has resistance \(R\). The wire is then uniformly stretched so its new length is \(2L\). Assuming the volume of the wire remains constant, what is the new resistance?

A wire has a resistance of \(5.0 \, \Omega\). If its length is doubled and its cross-sectional area is halved, what will be its new resistance?

A copper wire has a diameter of \(0.50 \, mm\) and a length of \(2.0 \, m\). If the resistivity of copper is \(1.68 \times 10^{-8} \, \Omega m\), calculate the resistance of the wire. Give your answer to two significant figures.

A copper wire has a diameter of \(0.50 \, \text{mm}\) and a length of \(2.0 \, \text{m}\). The resistivity of copper is \(1.68 \times 10^{-8} \, \Omega \text{m}\) at room temperature.
Calculate the resistance of the copper wire.

A heating element is made from a nichrome wire of length \(L\), diameter \(d\), and resistivity \(\rho\). It has a resistance of \(R\).
(a) Derive an expression for the resistance \(R\) in terms of \(L\), \(d\), and \(\rho\).
(b) If the length of the nichrome wire is halved to \(\frac{L}{2}\) and its diameter is doubled to \(2d\), determine the new resistance of the wire in terms of \(R\).
(c) Explain qualitatively how the resistance of a metal conductor changes with increasing temperature, and suggest a reason for this change at the microscopic level.