Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will measure the currents at two different points in the same circuit and investigate how the currents depend on the total resistance of the circuit. (a) (i) Set up the circuit as shown in Fig. 1.1. ammeter 2 x A wire L M N metre rule A ammeter 1 Fig. 1.1 There are crocodile clips at L, M and N. Place the crocodile clip at N so that the length x from N to M is approximately 60 cm. (ii) Measure and record the value of x. x = ...................................................... (iii) Close the switch. (iv) Record the current I1 given by ammeter 1. I1 = ................................................. [1] (v) Record the current I2 given by ammeter 2. I2 = ................................................. [2] (vi) Open the switch. (b) Change x and repeat (a) until you have six sets of readings of x, I1 and I2 where x is in For the range 0.200 m x 0.800 m. Examiner’s Use I2 1 Include values of and in your table. I1 x [9] I2 1(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] I1 x (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 (d) The quantities I1, I2 and x are related by the equation For Examiner’s Use I2 P = + Q I1 x where P and Q are constants. Using your answers from (c)(iii), determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (iv) Value for I1 < 200 mA, with consistent unit. [1] (v) Value for I2 with unit of current. [1] I2 > I1 [1] (b) Six sets of readings of I1, I2 and x scores 4 marks, five sets scores 3 marks etc. [4] Incorrect trend –1. Major help from Supervisor –2. Minor help from Supervisor –1. Range: xmax – xmin [ 0.500 m. [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. I / A or I(A), 1/x (m–1), I1/I2 Consistency: [1] All values of x must be given to the nearest mm. Significant figures: [1] All values of I2 / I1 must have the same significant figures as, or one more than, the least number of significant figures in raw I1 and I2 Calculation: [1] Values of I2 / I1 calculated correctly. (c) (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 must be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted on the graph grid. Diameter of plots must be Y half a small square. Check that the points are plotted correctly. Work to an accuracy of half a small square in both the x and y directions. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be scored. Judge by the scatter of all the points about a straight line. All points must be within ± 0.25 m–1 in the 1/x direction of a straight line. (ii) Line of best fit: [1] Judge by balance of all the 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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – October/November 2012 9702 35 (iii) Gradient: [1] The sign of the gradient must match the graph. 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. The method of calculation must be correct. y intercept: [1] Either: Correct read-off from a point on the line and substitution into y = mx + c. Read-off must be accurate to half a small square in both the x and y directions. Or: Correct read-off of the intercept directly from the graph. (d) Value of P = candidate’s gradient and value of Q = candidate’s intercept. [1] Do not allow a value presented as a fraction. Unit for P (m or cm or mm, consistent with value) and Q (no unit) correct. [1] [Total: 20]

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2 In this experiment, you will investigate how the motion of a spring depends on its length. (a) (i) Measure and record the diameter D of the coiled part of the spring as shown in Fig. 2.1. D Fig. 2.1 D = ................................................. [1] (ii) Estimate the percentage uncertainty in your value of D. percentage uncertainty = ................................................. [1] (b) (i) Place the metal strip through the spring as shown in Fig. 2.2. The length x of the coiled part of the spring below the metal strip should be approximately 1.5 cm. loop A metal strip x loop B Fig. 2.2 (ii) Measure and record x. x = ................................................. [1] (iii) Calculate the volume V inside the coiled part of the spring below the metal strip For using Examiner’s Use π D2 x V = . 4 V = ................................................. [1] (c) (i) Clamp the metal strip so that it is horizontal with loop A of the spring at the top. Gently hang a mass of 300 g from loop B, as shown in Fig. 2.3. Ensure that the base of the mass hangs approximately 20 cm above the bench. A metal strip B 300 g mass 20 cm benchbench Fig. 2.3 (ii) Slowly and gently pull the mass towards the bench by approximately 1 cm. For Examiner’s (iii) Release the mass and watch its movement. Use The mass will move up and then down, completing a cycle, as shown in Fig. 2.4. one complete cycle Fig. 2.4 (iv) Measure and record the time for at least 10 cycles. Record enough readings to determine an accurate value for the time T taken for one complete cycle. T = .............................................. s [2] (d) (i) Remove the mass from the spring. (ii) Remove the spring from the metal strip. (iii) Repeat (b)(i) making x approximately 1.0 cm. (iv) Measure and record x. x = ................................................. [1]

Mark scheme: 2 (a) (i) Value for D in range 10 to 20 mm to the nearest mm, with unit. [1] (ii) Percentage uncertainty in D based on an absolute uncertainty of 0.5, 1, 2 or 3 mm. [1] If repeated readings have been taken, then the absolute uncertainty can be half the range. Correct method used to calculate the percentage uncertainty. (b) (ii) Value of x to the nearest mm, in range 1.3 – 1.7 cm, with unit. [1] (iii) Correct calculation of V with consistent unit. [1] (c) (iv) Raw time values to 0.1 s or 0.01 s. Value of T in range 0.1 – 1.0 s. [1] Evidence of repeat measurements. [1] (d) (iv) Second value of x. [1] (e) Second value of T. [1] Second value of T < first value of T. [1] (f) (i) Correct calculation of two values of k. [1] (ii) Justification of significant figures in k linked to significant figures in D, x and time (not just “raw readings”). [1] (iii) Sensible comment relating to the calculated values of k, testing against a specified criterion. [1] GCE AS/A LEVEL – October/November 2012 9702 35 (g) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A two results not enough take more readings “repeat readings” on its and plot a graph/ own calculate more k values and compare few readings/ only one reading take more readings and (calculate) average k B parallax error in D/ use Vernier use string difficult to measure D because calipers/micrometer/travelling loop is in the way microscope to measure D* C V not accurate because measure thickness/diameter of D not internal diameter wire using micrometer use travelling microscope/Vernier calipers to measure D* D mass swings side-to-side/ horizontal movement/ moves in more than one plane/non- uniform oscillation E times are small/large use bigger mass light gates/ uncertainty in T human error/reaction improved timing method e.g. time/ motion/position sensor below time more cycles/ weight/video with timer/video and high frequency view frame-by-frame** oscillations F difficult to judge fixed/fiducial marker marker fixed to spring/ start of/end of/complete marker placed at oscillation improved timing method e.g. extreme(s) of oscillation motion/position sensor below weight/video with timer/video and light gates view frame-by-frame** G metal strip bends/ use stiffer strip/ strip not straight/ not horizontal thicker strip/support strip at both move spring/use ends. stronger strip * Credit in Bs or Cs, but not both. ** Credit in Es or Fs, but not both. [Total: 20]

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