Cambridge A Level Physics 9702 — 2020 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate an electrical circuit. (a) ● Place the 18 Ω resistor in component holder R. ● Set up the circuit shown in Fig. 1.1. 1.5 V d.c. X R X V Fig. 1.1 ● The resistor in R has resistance R. Record R. R = ............................................................Ω ● Close the switch. ● Record the voltmeter reading V. V = ............................................................... ● Open the switch. [1] (b) Change the resistor in R and repeat (a) until you have six sets of readings of R and V. Include your values from (a). 1 1 Record your results in a table. Include values of and in your table. R V [9] 1 1(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] V R (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 R are related by the equation 1 A = + B V R where A and B are constants. Using your answers in (c)(iii), determine values for A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (e) (i) Theory suggests that 2 B = E where E is the electromotive force (e.m.f.) of the cell. Determine E. E = ...................................................... V [1] (ii) The two other resistors in the circuit each have resistance X. When R = X, theory suggests that 1 3 = V E. Determine X. X = ..................................................... Ω [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of V with unit in the range 0.400–0.500 V. 1 1(b) Six sets of readings of R and V (different values) showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: Values of R must include 12 Ω and 18 Ω and 39 Ω. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1 / V / V–1 and R / Ω. 1 Consistency: All values of V must be given to the nearest 0.001 V (or 1 mV). 1 Significant figures: 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 V. 1 Calculation: Values of 1 / V are correct. 1 1(c)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. 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. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within 0.05 V–1 on the 1 / V axis of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. If there are 6 or more points, allow one anomalous point only if clearly indicated by the candidate. Line must not be kinked or thicker than half a small square. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow Δx / Δy. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be 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 1(d) Value of A = candidate’s gradient and value of B = candidate’s intercept. The values must not be fractions. 1 Unit for A correct (e.g. Ω V–1 or Ω mV–1) and unit for B correct (e.g. V–1 or mV–1). 1 1(e)(i) E calculated correctly using E = 2 / y-intercept or E = 2 / B. 1 1(e)(ii) X correctly determined e.g. calculation of 3 / E, read-off of the corresponding value of 1 / R from the graph, then calculation of X or using X = A / (3 / E – B) or using X = EA. 1

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2 In this experiment, you will investigate the equilibrium of a metre rule. (a) (i) You have been provided with a metre rule with two springs attached. The distance between one end of the metre rule and the string is L, as shown in Fig. 2.1. L tape string metre rule springs Fig. 2.1 Measure and record L. L = ......................................................... [1] L (ii) Calculate where n = 3. n L = ......................................................... [1] n (b) (i) ● Set up the apparatus as shown in Fig. 2.2. stand stand L metre rule with scale facing upwards n boss boss rod of clamp bench Fig. 2.2 ● Adjust the apparatus until the horizontal distance between the centres of the rods of L the clamps is equal to your value of n. ● Adjust the heights of the bosses so that the rule is horizontal and the springs are vertical and unstretched when the rule is held in position. ● Gradually release the rule by lowering your hand. The rule will tilt. ● The angle between the rule and the horizontal is θ, as shown in Fig. 2.3. θ rod of clamp Fig. 2.3 Measure and record θ. θ = ........................................................° [2] (ii) Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = ......................................................... [1] (iii) Calculate sin θ. sin θ = ......................................................... [1] (iv) Justify the number of significant figures that you have given for your value of sin θ. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] L(c) ● Calculate where n = 4. n L = ............................................................... n L ● Repeat (b)(i) and (b)(iii) using this value of n. θ = ............................................................. ° sin θ = ............................................................... [2]

Mark scheme: 2(a)(i) Value of L to the nearest mm in the range 98.5–99.5 cm with unit. 1 2(a)(ii) Correct calculation of L / 3. 1 2(b)(i) Measurement of θ to the nearest degree. 1 Value of θ in the range 0°─20°. 1 2(b)(ii) Percentage uncertainty in θ based on absolute uncertainty in the range 2°–5°. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(iii) Correct calculation of sin θ. 1 2(b)(iv) Justification for s.f. in sin θ linked to s.f. in θ. 1 2(c) Second value of θ. 1 Quality: Second value of θ > first value of θ. 1 2(d)(i) Two values of C calculated correctly. 1 2(d)(ii) Valid comment consistent with calculated values of C, testing against a criterion stated by the candidate. 1 2(e) Value of k correctly calculated and in the range 10–20 N m–1 and with consistent unit. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure θ with reason e.g. holding protractor and hand moves. C Rule slips on clamp. D Difficult to know when rule is horizontal. E Difficulty linked to setting L / n with a reason e.g. stands move suddenly/friction between bench and stands. F Difficult to hold one end of the rule and adjust the other end at the same time. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Mount protractor on block/use another ruler and use trigonometry to determine angle. C Use adhesive putty/tape on rod. D Use spirit level/another rule to ensure horizontal. E Method to ensure smooth movement of stands e.g. mount stands on wheels/rollers. F Use a third stand and clamp to hold the free end of the rule. 1 mark for each point up to a maximum of 4. 4

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