Cambridge A Level Physics 9702 — 2016 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the behaviour of an electrical circuit. (a) The positive terminals of C and the d.c. supply are already connected. Complete the circuit shown in Fig. 1.1, making sure that the positive terminals are connected as indicated on the diagram. d.c. supply + – + C R + V S Fig. 1.1 (b) (i) Switch S should be open. When the d.c. supply is switched on, the voltmeter reading will rise and become constant. Switch on the d.c. supply and record the voltmeter reading VS after approximately 60 s. VS = ....................................................V (ii) Calculate the value of 0.9VS. 0.9VS = ..............................................V [1] (c) (i) Close switch S. The voltmeter reading will fall to zero. (ii) Open S and measure the time t for the voltmeter reading to rise to a value VC of approximately 4.0 V. Record t and VC. t = .................................................... s VC = ....................................................V [1] (d) (i) Write down your value of 0.9VS from (b)(ii). 0.9VS = ....................................................V (ii) Repeat (c) for different values of VC in the range 0 to 0.9VS until you have six sets of values of t and VC. [8] (e) (i) Plot a graph of VC on the y-axis against t on the x-axis. [2] (ii) Draw a smooth curve through your points. [1] (f) (i) Calculate the value of 0.5VS. 0.5VS = ....................................................V (ii) Draw the tangent to your curve at VC = 0.5VS. [1] (iii) Determine the gradient and y-intercept of this tangent. gradient = ...................................................... y-intercept = ...................................................... [2] (g) The tangent has the equation VC = a t + b where a and b are constants. Use your answers in (f)(iii) to determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] (h) Calculate the value of T using the relationship VS T = 2a. T = ..................................................[2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (ii) 0.9VS calculated correctly and to the same number of s.f. as, or one more than, the s.f. of VS in (b)(i). [1] (c) (ii) Value for t in range 1.0 s to 9.0 s. [1] (d) (ii) Six sets of values for VC and t with correct trend scores 5 marks, five sets scores 4 marks etc. [5] Minor help from supervisor –1, major help from supervisor –2. Range: [1] Range of values to include VC ≤ 3.0 V and VC ≥ 8.0 V. Column headings: [1] Each column heading must contain a quantity and an appropriate unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. VC / V or VC (V). Consistency: [1] All values of t must be given to the nearest 0.1 s, or all to the nearest 0.01 s. (e) (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 must be no more than three large squares 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 (no “blobs”). Plotted points must be accurate to half a small square. (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate's curve (at least 5 points). There must be an even distribution of points either side of the curve 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. (f) (ii) Tangent drawn at VC = 0.5VS. Tangent must touch curve at the candidate’s value of 0.5VS from (f)(i). [1] (iii) Gradient: [1] The hypotenuse of the triangle used must be greater than half 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 x and y directions. y-intercept: [1] Either: Correct read-off from a point on the tangent is 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). (g) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] Correct units for a (e.g. V s–1) and b (s). [1] (h) Correct calculation of T. [1] Quality: T in the range 8.0 s to 14.0 s, with consistent unit. [1]

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2 In this experiment, you will investigate the relationship between the dimensions of a spring and its spring constant. You are provided with two lengths of copper wire with the same diameter. (a) Measure and record the diameter d of the wire. d = ..................................................[1] (b) (i) Wind one of the lengths of wire around the rod labelled A so that it makes a spring, as shown in Fig. 2.1. rod A Fig. 2.1 (ii) Slide the spring off the rod and then twist the ends to give a loop at each end, as shown in Fig. 2.2. loop loop Fig. 2.2 (iii) Count and record the number n of coils in your spring, and measure and record the outside diameter x of your spring, as shown in Fig. 2.3. Q coils [ Fig. 2.3 n = ...................................................... x = ...................................................... [2] (c) Estimate the percentage uncertainty in your value of x. percentage uncertainty = ..................................................[1] (d) Calculate the value of D using the expression D = x – d. D = ...................................................... (e) (i) Set up the apparatus as shown in Fig. 2.4, with the boss approximately 25 cm above the bench. VWDQG QDLO ERVV VSULQJ PDVV KDQJHU K1 EHQFK Fig. 2.4 (ii) Measure and record the height h1 of the bottom of the mass hanger above the bench. h1 = ..................................................[1] (iii) Add the 50 g mass to the mass hanger and measure the height h2 of the bottom of the mass hanger above the bench, as shown in Fig. 2.5. J PDVV K2 Fig. 2.5 h2 = ......................................................

Mark scheme: 2 (a) d in the range 0.5 mm to 0.9 mm, to nearest 0.1 mm or to 0.01 mm, with unit. [1] (b) (iii) Value for x in the range 11–19 mm, with unit. [1] Evidence of repeat readings of x. [1] (c) Absolute uncertainty in x in range 2 mm to 5 mm. 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] (e) (ii) h1 recorded to nearest mm, with consistent unit. [1] (iv) Correct calculation of k to the number of s.f. given by the candidate. [1] Value of k given to the same number of s.f. as, or one more than, the number of s.f. in (h1 – h2) or m, whichever is lower. [1] (f) Second values of x and n. [1] Second values of h1 and h2. [1] Quality: Value of (h1 – h2) for smaller x less than the value of (h1 – h2) for larger x. [1] (g) (i) Two values of c calculated correctly. [1] (ii) Valid comment consistent with the calculated values of c, testing against a criterion specified by the candidate. [1] (h) (i) Limitations [4] (ii) Improvements [4] Do not credit A Two readings are not enough to Take more readings and plot Repeat readings/ draw a conclusion graph/ few readings/ take more readings and only one reading /not compare c values enough readings for accurate value B d is small/ Use a micrometer (to measure Digital calipers large (percentage) uncertainty in diameter) d C n not an integer Estimate n to the nearest ¼ turn D Diameter not constant/ Method of making equally- Spring not straight coils vary in diameter/ spaced coils e.g. make small Use ‘factory’ spring coils not equally spaced/ marks/grooves on wooden rod coils not circular Use motor to wind spring by rotating rod E Difficult to measure diameter (x) Use thin ruler/graph paper with reason e.g. calipers distort placed between loops of spring coils/end of coil gets in the way of ruler F h1 – h2 small, so uncertainty Use larger mass/larger range of large masses Travelling microscope with reference to h1 – h2 Use wires of longer length to increase h1 – h2

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