A metal wire joins a power supply to a lamp. Its total resistance is $3.4\,\Omega$ and the metal’s resistivity is $2.6 \times 10^{-8}\,\Omega\,\text{m}$. The complete length of the wire is $59\,\text{m}$.
Demonstrate that the wire’s cross-sectional area is $4.5 \times 10^{-7}\,\text{m}^2$.
A potential difference of $1.8\,\text{V}$ is applied across the full length of the wire. Work out the current in the wire.
The free-electron number density in the wire is $6.1 \times 10^{28}\,\text{m}^{-3}$. Determine the mean drift speed of the free electrons in the wire.
A separate wire carries a current. One section of this wire is thinner than the remainder of the wire, as shown in Fig. 5.1.
State and explain qualitatively how the average drift speed of the free electrons in the thinner section compares with that in the rest of the wire.
State and explain whether the power dissipated in the thinner part is the same, less or more than the power dissipated in an equal length of the rest of the wire.
The resistances of the three resistors are $180\,\Omega$, $90\,\Omega$ and $30\,\Omega$.
Sketch a circuit diagram that shows how any two of these three resistors can be joined to produce a combined resistance of $60\,\Omega$ between the terminals shown. Make sure the resistor values are labelled on your diagram.
The three resistors are connected to a battery with electromotive force (e.m.f.) $12\,\text{V}$ and negligible internal resistance to make a potential divider circuit. This potential divider gives an output potential difference $V_{\text{OUT}}$ of $8.0\,\text{V}$. Fig. 5.2 displays the circuit diagram. On Fig. 5.2, add the resistance values for all three resistors and mark the potential difference $V_{\text{OUT}}$.
State and explain qualitatively how the average drift speed of the free electrons in the thinner part compares with that in the rest of the wire.
State and explain whether the power dissipated in the thinner part is the same, less or more than the power dissipated in an equal length of the rest of the wire.