Cambridge A Level Physics 9702 — 2016 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate how the current in a circuit changes as the resistance of the circuit is changed. (a) (i) Set up the apparatus as shown in Fig. 1.1. wooden strip wire nail + power supply wooden strip – A L Fig. 1.1 (ii) Measure and record the length L of the shorter wire. L = ..................................................[1] (b) (i) Complete the circuit as shown in Fig. 1.2. x + crocodile clip wire – A x Fig. 1.2 Each crocodile clip should be attached to a wire at the same distance x from the end of the wire, as shown in Fig. 1.2. (ii) Measure and record the distance x. x = ...................................................... (iii) Close the switch. (iv) Record the ammeter reading I. I = ..................................................[1] (v) Open the switch. (c) Change x and repeat (b) until you have six sets of readings of x and I. 1 Include values of in your table. I [9] 1(d) (i) Plot a graph of on the y-axis against x on the x-axis. [3] I (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (e) The quantities I and x are related by the equation 1 = – Px + Q I where P and Q are constants. Using your answers in (d)(iii), determine values for P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] (f) (i) The e.m.f. E of the d.c. power supply is given on the card. Record E. E = .................................................. V (ii) Theory suggests that R 3PL Q = + E 2 where R is the resistance of the resistor. Use values in (a)(ii), (e) and (f)(i) to determine the value of R. R = ..............................................Ω [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (ii) Value for L to the nearest mm with unit and in range 38.0 cm ≤ L ≤ 42.0 cm. [1] (b) (iv) Value of I with unit in the range 25 mA to 100 mA. [1] (c) Six sets of readings of x and I with correct trend scores 4 marks, five sets scores 3 marks etc. [4] Minor help from Supervisor –1, major help –2. Range of x: [1] ∆x ≥ 30.0 cm. Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The unit must conform to accepted scientific convention, e.g. 1 / I / A–1 or 1 / I (A–1) or 1/I / 1/A. Do not allow 1 / I (A). Consistency: [1] All values of I given to 0.1 mA. Significant figures: [1] Every value of 1 / I must be given to the same number of s.f. as (or one more than) the number of s.f. in the corresponding value of I. Calculation: [1] Values of 1 / I calculated correctly to the number of s.f. given by the candidate. (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. 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. Plotting of points: [1] All observations must be plotted. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to half a small square. Quality: [1] All points in the table must be plotted on the grid for this mark to be awarded. All points must be within 2.0 cm (to scale) on the x-axis of a straight line. (ii) Line of best fit: [1] 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. Allow one anomalous point only if clearly indicated by the candidate. Lines must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle used must be greater than half of the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-off from a point on the line and substituted into y = mx + c. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read off directly from the graph (accurate to half a small square). (e) P = –value of candidate’s gradient Q = value of candidate’s intercept. [1] Do not allow fractions. Unit for P correct (e.g. A–1 m–1, A–1 cm–1, A–1 mm–1, mA–1 m–1, mA–1 cm–1 or mA–1 mm–1). Unit for Q correct (e.g. A–1 or mA–1) and consistent with value. [1] (f) Value of R in the range 5 Ω to 20 Ω. [1]

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2 In this experiment, you will investigate the position of a wooden strip with several forces acting on it. (a) (i) Balance the wooden strip on the pivot as shown in Fig. 2.1. The distance between one end of the wooden strip and the pivot is C when the wooden strip is balanced. C string wooden strip A B pivot bench Fig. 2.1 (ii) Measure and record C. C = ..................................................[1] (iii) Measure and record the distance d between the end of the wooden strip and the centre of hole A as shown in Fig. 2.2. d A B Fig. 2.2 d = ..................................................[1] (iv) Calculate (C – d ). (C – d ) = ..................................................[1] (b) (i) Set up the apparatus as shown in Fig. 2.3 with the nail through hole A. stand boss stand nail wooden strip e string boss pulley mass hanger bench Fig. 2.3 Adjust the apparatus so that the string is parallel to the bench. The angle θ is the angle between the wooden strip and the stand. (ii) Measure and record θ. θ = ..................................................[1] (iii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1] (c) Calculate (tanθ – 1). Give your answer to a suitable number of significant figures. (tanθ – 1) = ..................................................[2] (d) Using hole B, repeat (a)(iii), (a)(iv), (b)(i), (b)(ii) and (c). d = ...................................................... (C – d ) = ...................................................... θ = ...................................................... (tanθ – 1) = ...................................................... [3]

Mark scheme: 2 (a) (ii) Value of C in the range 35.0 cm to 40.0 cm with unit. [1] (iii) Value of d to the nearest mm with unit in range 4.0 cm to 6.0 cm. [1] (iv) Correct calculation of (C – d). [1] (b) (ii) Value of θ to the nearest degree with unit, and θ < 90°. [1] (iii) Absolute uncertainty in θ in range 2° to 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] (c) Correct calculation of (tanθ – 1). Do not allow a unit. [1] Answer given to 2 s.f. or 3 s.f. [1] (d) Second value of d. [1] Second value of θ. [1] Quality: Second value of θ > first value of θ. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (f) (i) Limitations [4] (ii) Improvements [4] Do not credit A Two readings not enough to Take more readings and plot a Repeat readings/ draw a conclusion graph/ few readings/ take more readings and only one reading/ compare k values not enough readings for accurate value B Difficult to measure angle Method of providing vertical with reason e.g. lack of reference e.g. vertical reference use a plumbline/ line/parallax/nail in the drill hole at origin of protractor way/apparatus moves when and mount on nail/ protractor in place method of fixing protractor/ use a grid with angles marked/ larger protractor C Range of θ is too small More holes further apart D Difficult to measure C whilst Mark position of pivot/ balancing strip add scale to wooden strip E Difficulty in mechanical set Method of improvement e.g. up e.g. alignment of strip spirit level linked to string/axle and string/horizontal string of pulley/ (parallel to table) add weights to stands F Friction at nail (or axle of Lubricate the nail/pulley axle pulley)

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