CAIE Physics (9702)

2025 May/June
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Questions & Answers

Q1a.
Short Answer 1 mark

A graph is plotted of 1/V on the y-axis against n on the x-axis. Determine expressions for the gradient and y-intercept.

Model Answer:
gradient = C/(EA)
Explanation: Rearranging EA = V(nC + A) gives 1/V = (C/EA)n + 1/E, so the gradient is C/(EA).
Model Answer:
y-intercept = 1/E
Explanation: From 1/V = (C/EA)n + 1/E, the intercept at n = 0 is 1/E.
Q1b.
Structured 2 marks

Values of n and the two measured values of the maximum potential difference V1 and V2 are given in Table 2.1. Calculate and record values of V and 1/V in Table 2.1. Include the absolute uncertainties in V and 1/V.

Model Answer:
V = mean of V1 and V2; absolute uncertainty in V = half the range of V1 and V2. For the table values: n=2, V=4.25 V, 1/V=0.235 V^-1; n=3, V=3.70 V, 1/V=0.270 V^-1; n=4, V=3.25 V, 1/V=0.308 V^-1; n=5, V=2.90 V, 1/V=0.345 V^-1; n=6, V=2.60 V, 1/V=0.385 V^-1; n=7, V=2.35 V, 1/V=0.426 V^-1. Absolute uncertainties in V are ±0.05 V for each mean value, and corresponding uncertainties in 1/V are obtained from the uncertainty in V.
Explanation: The mean of the two readings is recorded for V, and the reciprocal is then calculated. The uncertainty in V is half the difference between the two readings.
Q1c(i).
Structured 2 marks

Plot a graph of 1/V against n. Include error bars for 1/V.

Model Answer:
A correctly plotted graph of 1/V against n with suitable scales, labelled axes, plotted points, and vertical error bars for 1/V.
Explanation: The graph must show the calculated reciprocal values against n, with error bars representing the uncertainty in 1/V.
Q1c(ii).
Structured 2 marks

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

Model Answer:
A straight line of best fit and a worst acceptable straight line drawn on the graph, both clearly labelled.
Explanation: This is a graphical construction question; the required response is the correctly drawn and labelled lines.
Q1c(iii).
Structured 2 marks

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

Model Answer:
gradient = value obtained from the best-fit line, with absolute uncertainty from the difference between the best-fit and worst acceptable gradients
Explanation: The gradient is found from the graph, and the uncertainty is estimated using the worst acceptable line method.
Q1c(iv).
Structured 2 marks

Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.

Model Answer:
y-intercept = value obtained from the best-fit line, with absolute uncertainty from the difference between the best-fit and worst acceptable intercepts
Explanation: The intercept is read from the graph and its uncertainty is estimated using the worst acceptable line.
Q1d(i).
Structured 2 marks

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of E and C. Include appropriate units. Data: A = (2.2 ± 0.2) mF

Model Answer:
E = 1/(y-intercept) V; C = gradient × E × A, with C in farads or millifarads as appropriate.
Explanation: From 1/V = (C/EA)n + 1/E, the intercept gives 1/E and the gradient gives C/(EA).
Q1d(ii).
Structured 1 mark

Determine the percentage uncertainty in your value of C.

Model Answer:
percentage uncertainty = (absolute uncertainty in C / C) × 100%
Explanation: Percentage uncertainty is calculated by dividing the absolute uncertainty by the measured value and multiplying by 100.
Q1e.
Structured 1 mark

The experiment is repeated with 10 capacitors, each of capacitance C, connected in parallel between P and Q. Determine the maximum potential difference V between P and Q.

Model Answer:
V = EA / (10C + A)
Explanation: Substitute n = 10 into the given relationship EA = V(nC + A) and rearrange for V.
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