Cambridge A Level Physics 9702 — 2025 May/June Paper 3 · Variant 7

1 In this experiment, you will investigate an electrical circuit. (a) • Set up the circuit shown in Fig. 1.1. 1.5 V d.c. V Fig. 1.1 • Record the voltmeter reading E. E = ......................................................... [1] (b) You have been provided with a metre rule with a wire attached. You have also been provided with two identical resistors placed in component holders, each labelled R. • Set up the circuit shown in Fig. 1.2. 1.5 V d.c. R R V wire F G metre rule L Fig. 1.2 • F and G are crocodile clips. The distance between F and G is L. Attach F and G to the wire so that L is approximately 30 cm. • Close the switch. • Record the value of L and the voltmeter reading V. L = ............................................................... V = ............................................................... • Open the switch. [1] (c) • Write down the value of E from (a). E = ............................................................... • Increase L by changing the position of F on the wire. Record L and V and repeat until you have six sets of values of L and V. Include your values from (b). E – V Record your results in a table. Include values of in your table. L [9] E – V (d) (i) Plot a graph of on the y‑axis against V on the x‑axis. [3] L (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y‑intercept of this line. gradient = ............................................................... y‑intercept = ............................................................... [2] (e) It is suggested that the quantities V and L are related by the equation E – V = PV – Q L where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (f) The resistance of R is R. Theory suggests that: • P and Q are both inversely proportional to R E • the graph cuts the x‑axis at a value of V = for all values of R. 2 A student repeats the experiment using two identical resistors, each with a lower value of R than in the original experiment. For the student’s experiment, draw a second line on the graph to show the expected results. Label this line W. [1] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Value of E to the nearest 0.001 V with unit. 1 1(b) Value of L with unit in the range 25.0–35.0 cm and V ˂ E. 1 1(c) Six sets of readings of L (different values) and V with correct trend (L increases as V decreases) and without help from 4 Supervisor scores 4 marks, five sets scores 3 marks, etc. Range of L: Lmin ⩽ 35.0 cm and Lmax ⩾ 80.0 cm. 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate. E – V The presentation of quantity and unit must conform to accepted scientific convention e.g. / V cm–1. L Consistency: All values of L must be to the nearest mm. 1 Significant figures: 1 E – V All values of must be given to 3 or 4 significant figures. L Calculation: 1 E – V Correct calculation of . L 1(d)(i) Axes: 1 Axes must be labelled with the required quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Plotting of points: 1 All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. Quality: 1 Trend of points must be positive. All points in the table (at least 5 points) must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within  0.02 V on the V-axis of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If 6 or more points are plotted and they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. 1(d)(iii) Gradient: 1 The hypotenuse of the triangle used must be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct, not x / y. Gradient sign on answer line must be consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line is substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(e) P = candidate’s gradient value and Q = –candidate’s intercept value. 1 Values must not be written as fractions or given to only one significant figure. Units for P: cm–1 or m–1 consistent with their readings 1 and units for Q: V cm–1 or V m–1 consistent with their readings. 1(f) Line W of larger gradient on left of original line, not crossing on graph grid. 1

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2 In this experiment, you will investigate the oscillations of a chain of paper clips. You have been provided with two spheres of modelling clay. (a) (i) The diameter of the smaller sphere is d, as shown in Fig. 2.1. d Fig. 2.1 Measure and record d. d = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of d. Show your working. percentage uncertainty = ......................................................% [1] (b) (i) • Set up the apparatus as shown in Fig. 2.2. stand x boss holding boss holding thin rod thin rod chain of paper clips bench Fig. 2.2 • Ensure that the rods are the same height above the bench. • Slide the paper clips at the ends of the chain onto the rods. • The distance between the centres of the rods is x. Position the stands so that x is approximately 70 cm. • Measure and record x. x = .................................................... cm [1] (ii) • Use the hook to attach the smaller sphere of modelling clay to the chain of paper clips as shown in Fig. 2.3. rod n paper clips hook modelling clay Fig. 2.3 • The number of paper clips between the hook and the end of the chain is n, as shown in Fig. 2.3. Place the hook so that n is 11. • Calculate N, where 3 2 N = n . Give your answer to three significant figures. N = ......................................................... [1] (c) • Pull the sphere towards you through a short distance. When the sphere is released, it will oscillate. • Take measurements to determine the period T of these oscillations. T = ......................................................... [2]

Mark scheme: 2(a)(i) Final value of d in the range 1.6–2.6 cm with unit and raw value(s) to the nearest mm. 1 2(a)(ii) Percentage uncertainty based on absolute uncertainty in d in range 2–5 mm. 1 Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty / value from (a)(i))  100. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 2(b)(i) Value of x in the range 65.0–75.0 cm to the nearest mm. 1 2(b)(ii) (N = ) 4.95 1 2(c) Value of T (on answer line) in the range 0.70–1.20 s with unit. 1 Repeats: At least two measurements of nT where n ⩾ 5. 1 2(d) Second values of d and x. 1 Second value of T. 1 Second value of T ˂ first value of T. 1 2(e)(i) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(e)(ii) Justification for significant figures in k linked to significant figures in time, d and x. 1 2(f) Correct calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 15%, leading to a consistent conclusion. 2(g)(i) A Two (sets of) readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few 4 readings”). B Difficult to measure d with a reason e.g. parallax error (with sphere on rule) / ruler not precise an instrument to use or large percentage uncertainty in d. C Difficult to measure x with a reason e.g. difficult to locate centres of rods / rods may not be parallel. D Difficult to measure time or T with a reason e.g. judge start / end / completion of an oscillation. E Difficulty with the chain during oscillation e.g. chain slips (along rod) during oscillation / chain falls off the rod whilst oscillating / other modes of oscillation of the chain / movement of rods or stands during oscillation of the chain / difficult to maintain x to be constant whilst chain oscillating. F Difficulty with sphere e.g. not a uniform sphere / sphere falling off (paper clip) / sphere changes shape when handled. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings (for different values of x and n) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B Use (vernier/digital) calipers or use blocks (either side of sphere) with detail. C Clamp rule (to measure x). D Video / film / record with timer in view or use marker at the centre of the oscillation. E Workable method to prevent chain from slipping e.g. groove in rod or workable method to mitigate unwanted modes of oscillation e.g. increase the number of paper clips or reduce the distance between the rods or use metal rods or clamp stands (to the bench). F Use a stiffer material for the balls e.g. use baked clay / metal balls or use a mould / preformed balls 1 mark for each point up to a maximum of 4.

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