Cambridge A Level Physics 9702 — 2024 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate an electrical circuit. You have been provided with a metre rule with a wire attached. You have also been provided with six identical resistors. Four of the resistors are connected in series and attached to a wooden block. The other resistors are labelled X and Z. (a) ● Set up the circuit shown in Fig. 1.1. 1.5 V d.c. X A F wooden block E metre rule wire H nail G n resistors y Fig. 1.1 (not to scale) ● E, F, G and H are crocodile clips. n resistors on the wooden block are connected in parallel with X. Connect F so that n = 2, as shown in Fig. 1.1. ● The distance between G and H is y. Attach H to the wire so that y is approximately 50 cm. ● Close the switch. ● Record n, y and the ammeter reading I. n = ............................................................... y = ............................................................... I = ............................................................... ● Open the switch. [2] (b) ● Connect Z as shown in Fig. 1.2. X E F Z Fig. 1.2 When Z is connected in parallel with the first of the resistors on the block, the total value of n is reduced by 0.5. For the arrangement in Fig. 1.2, the value of n is 1.5. ● Close the switch. ● Change the position of H on the wire until the value of I is as close as possible to your value in (a). ● Record n and y. n = ............................................................... y = ............................................................... ● Open the switch. ● Disconnect Z. [1] (c) Vary n by changing the position of F and connecting and disconnecting Z. For each value of n, change the position of H until the value of I is as close as possible to your value in (a). Repeat until you have six sets of values of n and y. Include your values from (a) and (b). n Record your results in a table. Include values of to two significant figures in your table. n + 1 [8] n(d) (i) Plot a graph of y on the y-axis against on the x-axis. [3] n + 1 (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 y and n are related by the equation Pn y = − + Q n + 1 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) Theory suggests that P X = Q C where the resistance X of resistor X is 12 Ω and C is the resistance of the whole circuit. Use your values in (e) to determine a value for C. C = ..................................................... Ω [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of y to the nearest mm in the range 45.0–55.0 cm with unit. 1 Value of I to the nearest 0.1 mA with unit. 1 1(b) Value of y in (b) greater than value of y in (a). 1 1(c) Six sets of readings of n (different values) and y with correct trend (average y decreases as n increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: Values of n must include 0.5 and 4. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. y / m. There must be no unit for n and no unit for n / (n + 1). 1 Significant figures: All values of n / (n + 1) must be given to 2 significant figures. 1 Calculation: Correct calculation of n / (n + 1). 1 1(d)(i) Axes: 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 x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used. Scales must not be awkward (e.g. 3:10 or fractions). 1 Plotting of points: 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 the x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be negative. It must be possible to draw a straight line that is within  0.02 on the n / (n + 1) axis of all plotted points. 1 Question Answer Marks 1(d)(ii) Line of best fit: ‘Best fit’ is judged by 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. Line must not be kinked or thicker than half a small square. Some candidates may choose to identify an anomalous point. If 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. There must be at least 5 points left after the anomalous point is disregarded. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used should 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. The method of calculation must be correct, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both the x and y directions. or Intercept read directly from the graph, with read-off at n / (n + 1) = 0, accurate to half a small square in y direction. 1 1(e) Value of P = – candidate’s gradient and value of Q = candidate’s intercept. The values must not be written as fractions or given to only one significant figure. 1 Units for P and Q: mm or cm or m consistent with y values given. 1 1(f) Correct calculation of C. 1

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2 In this experiment, you will investigate the oscillations of a rod. (a) (i) The length of the rod is L, as shown in Fig. 2.1. L Fig. 2.1 Measure and record L. L = ......................................................... [1] (ii) The mass of the rod is M. Measure and record M. M = ......................................................... [1] (iii) Calculate S, where ML2 S = . 12 S = ......................................................... [1] (iv) Justify the number of significant figures that you have given for your value of S. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Wrap one end of the copper wire tightly three times around the centre of the rod, as shown in Fig. 2.2. copper wire rod Fig. 2.2 ● Slide a 50 g slotted mass onto each end of the rod. ● Record the mass m on one end of the rod. m = ............................................................ g ● Adjust the positions of the masses so that they are equally spaced from the centre of the rod and their centres are approximately 3 cm apart, as shown in Fig. 2.3. You may need to use some of the adhesive putty to keep the masses in position. mass m mass m adhesive putty ≈ 3 cm Fig. 2.3 ● Set up the apparatus as shown in Fig. 2.4. clamp boss rubber band stand wire bench a a Fig. 2.4 ● Make a hook in the wire and place the hook on the rubber band. ● The distance between the centre of each mass and the wire is a. Adjust the position of the masses until the rod is parallel to the bench and each mass is the same distance a from the wire. ● Measure and record a. a = ............................................................... [1] (ii) Estimate the percentage uncertainty in your value of a. Show your working. percentage uncertainty = ..................................................... % [1]

Mark scheme: 2(a)(i) Value(s) of raw L to the nearest mm with unit. 1 2(a)(ii) Value(s) of M to the nearest 0.1 g or better with unit. 1 2(a)(iii) Correct calculation of S. 1 2(a)(iv) Justification for significant figures in S linked to significant figures in L and M. 1 2(b)(i) Value(s) of raw a to the nearest mm and final value in the range 1.20–1.80 cm with unit. 1 2(b)(ii) Percentage uncertainty in a based on absolute uncertainty in the range 2–10 mm. Correct method of calculation to obtain percentage uncertainty e.g. (absolute uncertainty / value from (b)(i))  100. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is shown clearly. 1 2(c) Value of T in the range 2.010.0 s with unit. 1 Repeats: At least two measurements of at least 3T. 1 2(d) Second values of m and a. 1 Second value of T  first value of T. 1 2(e) Two values of k calculated correctly. The final k values must not be written as fractions or given to only one significant figure. 1 2(f) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 10% leading to consistent conclusion. 1 Question Answer Marks 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure a with reason e.g. masses not parallel / masses too wide / difficult to judge or determine the centre of mass / parallax error / stem of wire not straight / masses are angled on rod. C Oscillations in other planes. D Difficulty with measuring T with reason e.g. difficult to judge when an oscillation starts/ends/is complete / T varies with amplitude or angle. E Difficulty with set-up e.g. wire or masses move on rod during oscillation / rod is unbalanced or not horizontal / difficult to make rod horizontal / difficult to position wire in the centre of rod. F Difficulty with adhesive putty with detail e.g. mass of adhesive putty is not taken into account / mass of adhesive putty is different on each side. G Difficulty with the angle or point of release e.g. making or judging or setting 90° angle / ensuring the angle is the same each time. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 2(g)(ii) A Take more readings (for different values of L) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Use thinner masses / use calipers (in order to measure a). D Workable method to measure T e.g. marker at centre of oscillation / video/film/record plus timer/view frame by frame. E Make a notch or groove in the rod / glue wire to the rod / tape wire to the rod / glue masses to the rod. F (Use balance to) measure mass of adhesive putty and add onto m / measure mass of adhesive putty and use the same mass of putty on each side / measure mass of putty and mass at the same time. G Use clamped protractor/clamped set square or use marker/pointer to note initial amplitude/angle. 1 mark for each point up to a maximum of 4. 4

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