CAIE Physics (9702)

A student investigates the discharge of capacitors in the circuit shown in Fig. 2.1. The capacitors have capacitances C and C The student closes the switch to charge the capacitors. The switch is opened and a stop-watch is started. The capacitors discharge through the resistor of resistance R. At a fixed time t the voltmeter reading V is recorded. The experiment is repeated for different values of C and C For each combination of C and C , the combined capacitance C is calculated. It is suggested that C and V are related by the equation V = I where I is the initial current in the resistor.

A graph is plotted of lnV on the y-axis against on the x-axis. Determine expressions for the gradient and y-intercept. gradient = y-intercept =

Values of C, C and V are given in Table 2.1. Table 2.1 / 10 / 10 / 10 V / V ln (V / V) 2.2 2.2 2.45 ± 0.05 2.2 3.3 2.75 ± 0.05 2.2 5.6 3.05 ± 0.05 3.3 3.3 3.10 ± 0.05 3.3 5.6 3.50 ± 0.05 5.6 5.6 3.85 ± 0.05 The relationship between C, C and C+ C Calculate and record values of / 10 and ln (V / V) in Table 2.1. Include the absolute uncertainties in ln (V / V).

(i) Plot a graph of ln (V / V) against / 10 Include error bars for ln (V / V).

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = [2] 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.850.900.951.001.051.101.151.201.251.301.351.40 In (V / V) / 10 To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.

Determine the y-intercept of the line of best fit. Do not include the absolute uncertainty. y-intercept =

Using your answers to

, determine the values of R and I . Include appropriate units. Data: t = (30 ± 1) s R = =

Determine the percentage uncertainty in R. percentage uncertainty in R = %

The experiment is repeated with the same value of t. Determine the combined capacitance C that gives a value of V of 1.20 V. C = F [1] [Total: 15]