State the meaning of an electric current.
A metal wire of length $L$ and cross-sectional area $A$ is shown in Fig. 6.1. $I$ is the current in the wire, $n$ is the number of free electrons per unit volume in the wire, $v$ is the average drift speed of a free electron and $e$ is the charge on an electron. State, in terms of $A$, $e$, $L$ and $n$, an expression for the total charge of the free electrons in the wire.
Use your answer in (i) to show that the current $I$ is given by the equation $I = nAve$.
A metal wire in a circuit has been damaged. The resistivity of the metal is unchanged, but the cross-sectional area of the wire is smaller over a length of $3.0\,\text{mm}$, as shown in Fig. 6.2. The wire has diameter $d$ at cross-section X and diameter $0.69d$ at cross-section Y. The current in the wire is $0.50\,\text{A}$. Determine the ratio $\dfrac{\text{average drift speed of free electrons at cross-section Y}}{\text{average drift speed of free electrons at cross-section X}}$.
The main section of the wire with cross-section X has resistance per unit length $1.7 \times 10^{-2}\,\Omega\,\text{m}^{-1}$. For the damaged part of the wire, calculate the resistance per unit length.
For the damaged section of the wire, calculate the power dissipated.
The diameter of the damaged part of the wire is reduced again. Assume that the current in the wire stays constant. State and explain qualitatively any change to the power dissipated in the damaged length of the wire.