Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will determine the resistivity of a metal. (a) ● Set up the circuit shown in Fig. 1.1. 3 V d.c. V Fig. 1.1 ● Record the voltmeter reading E. E = ........................................................... V ● Set up the circuit shown in Fig. 1.2. 3 V d.c. nail x Q 22 Ω P V metal wire wooden strip Fig. 1.2 (not to scale) ● P and Q are crocodile clips. The distance between the nail and Q is x, as shown in Fig. 1.2. Adjust the position of Q until x is approximately 45 cm. ● Close the switch. ● The voltmeter reading is V. Measure and record x and V. x = ............................................................... V = ............................................................... ● Open the switch. [1] (b) Change x by adjusting the position of Q on the wire. Use six different values of x. For each value of x, measure V. 1 Record your results in a table. Include values of in your table. V [8] 1(c) (i) Plot a graph of on the y-axis against x on the x-axis. [3] V (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (d) It is suggested that the quantities V and x are related by the equation 1 = Ax + B V where A and B are constants. Using your answers in (c)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [1] (e) (i) Use a micrometer to measure the diameter d of the wire. d = ......................................................... [2] (ii) It is suggested that A is given by the equation 4ρ A = – πd 2ER where R is 22 Ω and ρ is the resistivity of the metal. Using your answers in (a), (d) and (e)(i), determine a value for ρ. Give an appropriate unit. ρ = ......................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value of E in the range 2.00–3.50 V. 1 1(b) Six sets of readings of x and V with the correct trend (V increases as x increases) and without help from the Supervisor 3 scores 3 marks, five sets scores 2 marks etc. Range: x ⩾ 70.0 cm. 1 Column headings: 1 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. 1 / V / V–1. Consistency: 1 All values of x must be given to the nearest millimetre. Significant figures: 1 All values of 1 / V must be given to the same number of s.f. as (or one more than) the number of s.f. in the raw V values. Calculation: Values of 1 / V are correct. 1 1(c)(i) Axes: 1 Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings must be no more than 2 cm (one large square) apart. 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 All points in the table must be plotted (at least 5) on the grid for this mark to be awarded. Trend of points must be negative. It must be possible to draw a straight line that is within  5 cm (to scale) on the x axis of all plotted points. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Candidates do not need to identify an anomalous point. However if there is a point off trend, it may be identified as anomalous by circling or labelling it. There must be at least 5 points left after one anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1(c)(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 matches graph drawn. y-intercept: 1 Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square. 1(d) Value of A = candidate’s gradient value and value of B = candidate’s intercept value. 1 Values must not be written as fractions. 1(e)(i) Value of d in the range 0.290 mm–0.340 mm and all raw values given to either 0.01 mm or all to 0.001 mm with unit. 1 Measurement of d repeated. 1 1(e)(ii) correctly calculated. 1 Correct unit (e.g.  m). 1

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2 In this experiment, you will investigate the extension of two springs. (a) (i) ● Set up the apparatus as shown in Fig. 2.1. stand boss clamp springs L1 mass hanger bench Fig. 2.1 ● The length L1 of the spring combination is measured from the top coil of the top spring to the bottom coil of the bottom spring, as shown in Fig. 2.1. Measure and record L1. L1 = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of L1. Show your working. percentage uncertainty = ..................................................... % [1] (iii) ● Add the slotted mass to the mass hanger. ● The new length of the spring combination is L2. Measure and record L2. L2 = ............................................................... ● The spring constant k is given by the equation W k = (L2 – L1) where W is 0.981 N. Calculate k. k = ............................................................... ● Remove the slotted mass and the mass hanger from the springs. [1] (iv) Justify the number of significant figures that you have given for your value of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Use the balance to measure and record the total mass M of the four smaller steel nuts. M = ............................................................... ● The volume V of the four nuts is given by the equation M V = ρsteel where the density ρsteel of steel is 7.8 g cm–3. Calculate V. V = ............................................................... [2] (ii) ● Set up the apparatus using the four smaller nuts as shown in Fig. 2.2. springs Lair paper clip four nuts Fig. 2.2 ● Bend the paper clip to hold the four nuts. ● The length of the spring combination is Lair . Measure and record Lair . Lair = ............................................................... ● Gently lower the nuts into the oil until they are submerged but not touching the bottom of the beaker, as shown in Fig. 2.3. Loil beaker oil Fig. 2.3

Mark scheme: 2(a)(i) Final value L1 in the range 10.0 cm to 20.0 cm and raw values to the nearest millimetre with unit. 1 2(a)(ii) Absolute uncertainty in L1 in the range 2–6 mm. 1 If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to find percentage uncertainty. 2(a)(iii) k calculated correctly. 1 2(a)(iv) Justification for number of significant figures in k linked to significant figures in W and (L2 – L1). 1 2(b)(i) Value of M in range 10 g ⩽ M ⩽ 100 g with unit. 1 Correct calculation of V. 1 2(b)(ii) Value of Loil with Loil < Lair. 1 2(b)(iii) Second values of M, Lair and Loil. 1 Second value of Lair is larger than first value of Lair. 1 2(c) Two values of Z calculated correctly. The final Z values must not be written as fractions. 1 2(d) Calculation of percentage difference between candidate’s two Z values. 1 Comparison of percentage difference with 5% leading to a consistent conclusion. 2(e) oil calculated with correct unit (e.g. kg m–3). 1 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficult to measure any L with a reason e.g. parallax error/hard to judge the end of the spring/hard to hold rule (still)/rule disturbs springs/rule not vertical. C (Lair – Loil) is small so large uncertainty/large percentage uncertainty in (Lair – Loil). D Volume or mass of paper clip not taken into account. E k determined on one result. F Small difference between (Lair – Loil) values for the small and large nuts. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings and plot a graph or take more readings and compare Z values (not “repeat readings” on its own). 4 B Method to improve the measurement of L e.g. use white paper or lined or grid sheet behind spring/clamp rule/use clamped pointers/add marker(s) at the ends of the spring. C Use (vernier) calipers/travelling microscope or use larger (bigger) nuts / more nuts. D Use a thinner or lighter paperclip/use nylon or cotton thread or measure the mass of the paperclip (with or without nuts). E Method to improve determination of spring constant e.g. plot a force–extension graph (and find the gradient). F Extend the range between the size of the nuts or use a spring with a smaller k value/less stiff spring. 1 mark for each point up to a maximum of 4.

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