Cambridge A Level Physics 9702 — 2025 May/June Paper 5 · Variant 1

1 Fig. 1.1 shows a thin coil of cross-sectional area A and length l connected to a resistor of resistance S and two terminals. l S Fig. 1.1 An alternating voltage is applied to the terminals. The peak value of the alternating voltage is E and the frequency is f. The peak value of the potential difference V across the resistor is determined using an oscilloscope. It is suggested that V is related to f by the relationship ES KAN 2f = V l where N is the number of turns on the coil and K is a constant. Plan a laboratory experiment to test the relationship between V and f. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine a value for K. In your plan you should include: • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken. 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Mark scheme: Question Answer Marks 1 Defining the problem vary f and measure V or f is the independent variable and V is the dependent variable 1 keep E constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • circuit with a.c. supply • oscilloscope connected in parallel with the resistor • workable circuit • oscilloscope and a.c. supply labelled labelled signal generator or variable frequency power supply connected across the terminals 1 method to determine V or E from oscilloscope, e.g. multiply amplitude / height of wave by y-gain on oscilloscope 1 method to determine f from oscilloscope, e.g. determine period T by multiplying number of divisions in 1 cycle or horizontal 1 distance in 1 cycle by the time base and f = 1 / T Method of Analysis 1 1 1 plot a graph of against f or equivalent, e.g. f against V V Allow logarithms e.g. lg V against lg f. relationship valid if a straight line is produced passing through the origin 1 (for lg V against lg f: relationship valid if a straight line is produced with gradient = −1) 1 1 1 1 against f f against V V l ES l ES 1 K =  gradient K = 2  2 AN AN gradient El S − y -intercept (for lg V against lg f: K =  10 ). AN 2 Additional detail including safety considerations 6 D1 precaution linked to hot coil or hot resistor or prevention of burns from coil or resistor, e.g. use gloves / switch off power supply when not measuring V to prevent burns from coil / resistor D2 keep N and A and l and S constant D3 method to keep S constant, e.g. switch off power supply between readings to prevent heating of resistor or to allow resistor to cool d 2 D4 method to determine A, e.g. use calipers / micrometer to measure diameter (of coil) / d and A= 4 D5 repeat measurements of diameter d along the length of the coil / in different directions and determine the average value of d D6 method to determine the value of S, e.g. separate circuit diagram showing resistor connected to ohmmeter, or circuit diagram showing resistor connected to a power supply with an ammeter and voltmeter and S = V / I D7 measure l with a ruler / calipers D8 oscilloscope drawn connected across terminals / across signal generator and description to determine E D9 adjust y-gain for maximum amplitude or adjust time base for length of one wave or measure n waves and divide measured time by n 1 D10 method to keep E constant, e.g. check p.d. and alter supply or method to keep l constant, e.g. tape coil or method to keep A constant, e.g. wind wire on a cylinder

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2 A student investigates an electrical circuit. The circuit is set up as shown in Fig. 2.1. Z A P Q Fig. 2.1 A battery of negligible internal resistance is connected to a resistor of resistance Z. Five resistors, each of resistance R, are connected in parallel between P and Q. The switch is closed. The total current I in the circuit is measured using the ammeter. The experiment is then repeated by changing the number n of resistors, each of resistance R, connected in parallel between P and Q. It is suggested that I and n are related by the equation R E = I + ( n Z) where E is the electromotive force (e.m.f.) of the battery. 1 1 (a) A graph is plotted of on the y-axis against on the x-axis. I n Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] 1 (b) Values of n, and I are given in Table 2.1. n Table 2.1 1 1 n I / μA / 103 A–1 n I 5 0.200 455 ± 5 6 0.167 525 ± 5 7 0.143 580 ± 5 8 0.125 635 ± 5 9 0.111 685 ± 5 11 0.0909 765 ± 5 1 1 Calculate and record values of / 103 A–1 in Table 2.1. Include the absolute uncertainties in . I I [2] 1 1 1(c) (i) Plot a graph of / 103 A–1 against Include error bars for . [2] I n. I (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) R 1 gradient = E Z y-intercept = E 2(b) 1 1 / 103 A–1 I 2.20 or 2.198 1.90 or 1.905 1.72 or 1.724 1.57 or 1.575 1.46 or 1.460 1.31 or 1.307 1 Values of / 103 A–1 correct as shown above. I 2(b) 1 1 Uncertainties in / 103 A–1 from  0.02 or  0.03 decreasing to  0.01. I 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. 1 1 Error bars in plotted correctly. I All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Thickness of the line must be less than half a small square. Do not accept line from top point to bottom point. Line must pass between (0.101, 1.40) and (0.104, 1.40) and between (0.189, 2.10) and (0.194, 2.10) Worst acceptable straight line drawn (steepest or shallowest possible line that passes through all the error bars). 1 Thickness of the line must be less than half a small square. All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient determined of worst acceptable line with clear substitution of data points into y / x. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point with consistent power of ten in m and y into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. 1 uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) Do not accept ECF from false origin method. 2(d)(i) R determined using gradient and R and Z given to 2 or 3 significant figures. 1 R = gradient  5.8 Z determined using y-intercept and R and Z given with units with appropriate powers of ten. 1 Z = y-intercept  5.8 unit of R:  or V A–1 unit of Z:  or V A–1 2(d)(ii) Percentage uncertainty determined using E = 0.2 (V) with method shown. 1  E gradient  R % =  +   100  E gradient  or  0.2 gradient  R % =  +   100  5.8 gradient  2(e) I determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d)(i) with correct substitution. 1 1 I = gradient +y -intercept 20 or E I =  R   +Z   20 

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