A student investigates the discharge of a capacitor in the circuit shown in Fig. 2.1. [Figure 2.1] The student closes the switch and charges the capacitor. The switch is opened and a stop-watch is started. The capacitor discharges through the two resistors of resistance R₁ and R₂ connected between P and Q. At a fixed time t the potential difference V across the capacitor is measured. The experiment is repeated for different values of R₁ and R₂. It is suggested that V, R₁ and R₂ are related by the equation In(V/E) = -t / (C(R₁ + R₂)) where E is the electromotive force (e.m.f.) of the battery and C is the capacitance of the capacitor.

1. (a)A graph is plotted of In V on the y-axis against 1/(R₁ + R₂) on the x-axis. Determine expressions for the gradient and y-intercept.[2]
2. (b)Values of R₁, R₂, V and In V are given in Table 2.1. Each resistance value has a percentage uncertainty of ±5%. [Table 2.1] Calculate and record values of (R₁ + R₂)/kΩ and 1/(R₁ + R₂)/10⁻⁶Ω⁻¹ in Table 2.1. Include the absolute uncertainties in (R₁ + R₂) and 1/(R₁ + R₂).[2]
3. (c)(i)Plot a graph of In (V/V) against 1/(R₁ + R₂)/10⁻⁶Ω⁻¹. Include error bars for 1/(R₁ + R₂).[2]
4. (c)(ii)Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled.[2]
5. (c)(iii)Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.[2]
6. (c)(iv)Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.[2]
7. (d)(i)Using your answers to (a), (c)(iii) and (c)(iv), determine the values of C and E. Include appropriate units. Data: t = (60 ± 1)s[2]
8. (d)(ii)Determine the percentage uncertainty in C.[1]
9. (e)The experiment is repeated using the same capacitor. Determine the value of (R₁ + R₂) that would give a value of V of 5.0V at time t = 60s.[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.