Paper 4 Current Electricity Fundamentals Answers

Q1 Resistivity experiment

1. Plot $R$ against $L$ for constant cross-sectional area. [2]
2. From $R=\rho L/A$, gradient $=\rho /A$, so $\rho =A\times$ gradient. [2]
3. Measure diameter at several positions and average; avoid heating by using small current; ensure good contacts; measure length between contact points; zero/check meters. [2]

Q2 Internal resistance graph

1. Axes and units [1]; suitable scale [1]; accurate plots [2]; best-fit straight line [1]. [5]

2. From $V=\mathcal{E}-Ir$, the vertical intercept is $\mathcal{E}$. The fitted intercept is approximately $1.58\mathrm{V}$. [2]
3. The gradient is $-r$. The fitted gradient is approximately $-0.420\mathrm{V}{\mathrm{A}}^{-1}$, so $r\approx 0.420\Omega$. [2]
4. Large current causes internal heating and polarisation, changing $r$ and the emf during the measurement; prompt readings with the switch open between readings reduce this drift and avoid damage. [2]
5. A constant voltmeter offset shifts all $V$ readings and therefore changes the vertical intercept/emf by that offset, but does not change the gradient or derived internal resistance. [2]