Cambridge A Level Physics 9702 — 2013 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will determine the resistivity of a metal in the form of a wire. Use (a) (i) Measure and record the diameter d of the short sample of wire that is attached to the card. You may remove the wire from the card. d = ..................................................[1] (ii) Calculate the cross-sectional area A of the wire, in m2, using the formula A = π d 2 . 4 A = ................................................. m2 (b) (i) Use the wire attached to the metre rule, one of the voltmeters and one of the resistors to set up the partial circuit shown in Fig. 1.1. + – l metre rule K L wire V Fig. 1.1 There are two crocodile clips, one labelled K and the other labelled L. Place K and L so that the distance l between them is approximately 30 cm. (ii) Measure and record the distance l between K and L. l = ...................................................m (iii) Use the other resistor and the other voltmeter to complete the circuit shown in For Fig. 1.2. Examiner’s Use + – l l K L M V V voltmeter voltmeter reading V1 reading V2 Fig. 1.2 (iv) Place the crocodile clip M at a distance l from L. The value of l should be the same as in (b)(ii). (c) (i) Switch on the power supply. (ii) Record the voltmeter readings V1 and V2 as shown in Fig. 1.2. V1 = ....................................................V V2 = ....................................................V [1] (iii) Switch off the power supply. (d) Change l and repeat (b)(ii), (b)(iv) and (c) until you have six sets of readings of l, V1 For Examiner’s and V2. For each set of readings, distances KL and LM should both be l. Use V1 Include values of in your table. V2 [10] V1(e) (i) Plot a graph of on the y-axis against l on the x-axis. [3] V2 (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] For Examiner’s Use (f) The quantities V1, V2 and l are related by the equation For V1 Examiner’sUse = Pl + Q V2 where P and Q are constants. (i) Use your answers in (e)(iii) to determine values for P and Q. P = ................................................m–1 Q = ...................................................... [1] (ii) The resistivity ρ of the material of the wire, in Ω m, can be found using the relationship ρ = PAR where R = 10 Ω. Use your answers in (a)(ii) and (f)(i) to calculate a value for ρ. ρ = ...........................................Ω m [1] You may not need to use all of the materials provided. For Examiner’s

Mark scheme: 1 (a) (i) Value for d in the range 0.15 mm ≤ d ≤ 0.25 mm, with unit. [1] (c) (ii) Values of V1 and V2 , and V1 ˃ V2. [1] (d) Six sets of readings of l, V1 and V2 scores 5 marks, five sets scores 4 marks etc. [5] Major help from Supervisor –2. Minor help from Supervisor –1. Range: ∆l ≥ 30 cm. [1] 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. l / m or l (m) Consistency: [1] All values of raw l must be given to the nearest mm. Significant figures: [1] Significant figures for every row of V1/V2 must be the same as, or one more than the least number of significant figures used in V1 and V2. Calculation: [1] Values of V1/V2 calculated correctly. (e) (i) Axes: [1] 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. Plotting of points: [1] All observations in the table must be plotted. Diameter of plotted point must be ≤ half a small square (no “blobs”). Work to an accuracy of 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 0.05 (to scale) on the y-axis V1/V2 from 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. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – October/November 2013 9702 31 (iii) Gradient: [1] The hypotenuse of the triangle must be at least 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. y-intercept: [1] Either: Check 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: Check read-off of the intercept directly from the graph. (f) (i) Value of P = candidate’s gradient. Value of Q = candidate’s intercept. [1] (ii) Value of ρ in range 1.0 – 20.0 × 10–7 Ω m [1] [Total: 20]

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2 In this experiment, you will investigate the change in shape of a rubber band when masses Use are hung from it. (a) Set up the apparatus as shown in Fig. 2.1. rubber band boss rod of clamp stand bench Fig. 2.1 The rods of the two clamps must be at the same height above the bench. Position the stands so that the rubber band has no slack. (b) Measure and record the mass m of the mass hanger. m = ..................................................[1] (c) (i) Suspend the mass hanger from the centre of the lower part of the rubber band as For shown in Fig. 2.2. Examiner’s Use e mass m Fig. 2.2 (ii) Measure and record the angle θ as shown in Fig. 2.2. θ = ..................................................[2] (iii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1] θ (iv) Calculate tan 2. θ tan = ..................................................[1] 2 θ (v) Calculate tan2 2. θ tan2 = ...................................................... 2 (d) (i) Add the slotted mass to the mass hanger. For Measure and record the total mass m of the mass hanger and slotted mass. Examiner’s Use m = ..................................................[1] (ii) For this total mass, repeat (c)(i), (c)(ii), (c)(iv) and (c)(v). θ = ...................................................... θ tan = ...................................................... 2 θ tan2 = ...................................................... 2 [2] (e) Remove the slotted mass from the mass hanger. Measure and record the angle θ. θ = ..................................................[1]

Mark scheme: 2 (b) Value of m to the nearest 1 g or better with consistent unit. [1] (c) (ii) Measurement of raw θ to nearest degree with unit. [1] Evidence of repeat readings for θ. [1] (iii) Percentage uncertainty in θ based on absolute uncertainty of 2 to 5° (or half the range provided this is not zero), and correct method of calculation. [1] (iv) Correct calculation of tan (θ / 2). [1] (d) (i) Second value of m > first value of m. [1] (ii) Second value of θ. [1] Quality: second value of θ ˂ first value of θ. [1] (e) Value of θ. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in m and θ. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – October/November 2013 9702 31 (g) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings not enough (to draw Take more readings and plot a repeat readings / a conclusion graph / take more readings and ‘few readings’ / ‘take calculate more k values and more readings and compare calculate average’ / ‘only one reading’ / ‘repeat readings’ on its own B Difficult to measure θ because Tie thread to centre of bottom of hook of mass (hanger) in the way / rubber band and hang mass thick band from it C Difficult to hold the protractor Improved method to measure θ steady / parallax error reading e.g. project image of stretched angle / protractor rubber band onto a screen / mark on board / measure lengths and calculate θ clamp protractor / take picture or video and measure angle D Rubber band stretches over time Take readings quickly / remove mass from rubber band between readings E Stands moved / rods twist when Method of preventing movement loads attached to rubber band of stands / clamp stands to bench / use nails in board F Difficult to locate centre of band Method of locating and mark centre e.g. measure and mark centre G Change in θ small Larger range of masses [Total: 20]

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