A copper wire $P$ with a cylindrical shape and length $0.24\,\text{m}$ is illustrated in Fig. 6.1. The current in the wire is $0.85\,\text{A}$. The resistance of the wire is $3.3\,\text{m}\Omega$. The total number of charge carriers, $N$, in the wire is $2.6 \times 10^{22}$. The resistivity of copper is $1.8 \times 10^{-8}\,\Omega\,\text{m}$.
(a)[2]
Calculate the potential difference across the two ends of the wire.
(b(i))[2]
Show that the wire's cross-sectional area is $1.3 \times 10^{-6}\,\text{m}^2$.
(b(ii))[1]
Show that the number density of charge carriers in the wire is $8.3 \times 10^{28}\,\text{m}^{-3}$.
(b(iii))[2]
Calculate the average drift speed of the charge carriers (electrons) in the wire.
(c(i))[4]
State and explain how the resistance of wire Q compares with the resistance of wire P.
(c(ii))[2]
On Fig. 6.3, sketch a graph of the variation of the average drift speed of the charge carriers with distance from end X of wire Q.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use of $V = IR$” …