Cambridge A Level Physics 9702 — 2020 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate combinations of resistors in an electrical circuit. Fig. 1.1 shows how resistors of resistance 68.0 Ω can be arranged to give different values of total resistance R. resistor arrangement R / Ω 68.0 136 204 34.0 22.7 45.3 102 Fig. 1.1 (a) ● Set up the circuit as shown in Fig. 1.2 with a resistor of resistance 68.0 Ω between F and G. A X F G Fig. 1.2 ● Record the total resistance R between F and G. R = ........................................................... Ω ● Close the switch. ● Record the ammeter reading I. I = ............................................................... ● Open the switch. [1] (b) Use six different arrangements of the 68.0 Ω resistors to provide six different total resistances between F and G. 1 For each arrangement, record R and I in a table. Include values of in your table. I [10] 1(c) (i) Plot a graph of on the y-axis against R 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] (d) It is suggested that the quantities I and R are related by the equation 1 R X = + I E E where E is the electromotive force (e.m.f.) of the power supply and X is the resistance of resistor X. Using your answers to (c)(iii), determine values for E and X. Give appropriate units. E = ............................................................... X = ............................................................... [3] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) 1 1(b) Six (or more) sets of readings of R and I (different values of R) with the correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc. 5 Range: Must use R = 204 Ω and 22.7 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 / I (mA–1). 1 Consistency of presentation: All raw values of I must be given to 0.1 mA or all to 0.01 mA. 1 Significant figures: All values of 1 / I must be given to the same number of s.f. as (or one more than) the number of s.f. in raw I. 1 Calculation: Values of 1 / I are correct. 1 1(c)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). 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 must be plotted (at least 5) on the grid for this mark to be awarded. Trend of points must be correct. It must be possible to draw a straight line that is within ±4 Ω (to scale) on the R axis (normally x-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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Lines 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. Method of calculation must be correct, e.g. not Δx / Δy. Gradient sign on answer line matches graph drawn. 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 substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at R = zero, accurate to half a small square. 1 1(d) E = 1 / gradient 1 X = E × y-intercept or X = y-intercept / gradient 1 Units for E and X correct (e.g. V and Ω). 1

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2 In this experiment, you will investigate the equilibrium of an L-shaped card. (a) (i) The dimensions p, q and w of the card are shown in Fig. 2.1. w p q card Fig. 2.1 (not to scale) Measure and record lengths p, q and w. p = ......................................................... cm q = ......................................................... cm w = ......................................................... cm [2] 2q (ii) Calculate . p + q 2q = ......................................................... [1] p + q (b) (i) ● Set up the apparatus as shown in Fig. 2.2. pin in cork held in clamp stand paper clip boss card bench Fig. 2.2 (not to scale) ● Adjust the position of the paper clip so that the top edge of the card is horizontal, as shown in Fig. 2.3. d Fig. 2.3 (not to scale) ● The distance d is the distance from the centre of the paper clip to the right-hand edge of the card when the top edge of the card is horizontal. ● Measure and record d. d = ................................................... cm [1] (ii) Estimate the percentage uncertainty in d. Show your working. percentage uncertainty = ......................................................... [1] (iii) Calculate (w – d ). (w – d ) = ................................................... cm [1] (c) (i) Explain how you would accurately reduce q to half of its original value. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (ii) ● Remove the card from the paper clip. ● Cut the card so that q is half of its original value. ● Measure and record the new value of q. q = ......................................................... cm 2q ● Calculate . p + q 2q = ............................................................... p + q [1] (iii) Repeat (b)(i) and (b)(iii). d = ......................................................... cm (w – d ) = ......................................................... cm [2]

Mark scheme: 2(a)(i) p = 7.0 ± 0.2 cm q = 21.0 ± 0.2 cm w = 24.0 ± 0.2 cm 1 All raw values recorded to the nearest millimetre. 1 2(a)(ii) Correct calculation of 2q p q + . 1 2(b)(i) Value of d. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty Δd in the range 2–5 mm. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(iii) Value of (w – d) correctly calculated from w and d. 1 2(c)(i) Valid method, e.g. measure q / 2 in several places and draw a straight line with a ruler. 1 2(c)(ii) Second q recorded to the nearest mm and half original value of q ± 1 mm. 1 2(c)(iii) Second value of d recorded. 1 Second value of d is larger than first value of d. 1 2(d)(i) Two values of k calculated correctly. The final k values must not be fractions. 1 2(d)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to judge when top edge of card is horizontal/difficult to keep card horizontal. C Difficult to accurately locate the centre of the paper clip, e.g. clip too large/clip not vertical/sides of clip not straight. D Difficulty with the attachment, e.g. paper clip does not grip/card falls. E Difficult to measure d with reason, e.g. touching disturbs equilibrium/ruler held by hand in mid-air/parallax error. F Card bends easily or corners on card may not be at right angles. 1 mark for each point up to a maximum of 4. 4 2(e)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Method to improve judgement of horizontal, e.g. use of spirit level/clamped ruler with detailed method to ensure horizontal/place a grid behind the apparatus with method to ensure horizontal/turn off air conditioning. C Method to improve location of centre of paper clip, e.g. use narrower paper clip/measure to either side of clip and average/use calipers to measure width of clip. D Improved method of suspension, e.g. place pin through card/hole with needle/add adhesive putty. E Improved method to measure d, e.g. clamp ruler/write scale on card/carefully remove with paper clip and measure on bench. F Use of named more rigid material or detailed use of a set square or protractor. 1 mark for each point up to a maximum of 4. 4

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