Cambridge A Level Physics 9702 — 2021 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate combinations of resistors in an electrical circuit. (a) Fig. 1.1. shows an electrical circuit. 3 V d.c. Z A R1 R2 Fig. 1.1 ● Set up the circuit shown in Fig. 1.1 using R1 = 33 Ω and R2 = 82 Ω. R1R2 ● Calculate . (R1 + R2) R1R2 = ............................................................Ω (R1 + R2) ● Close the switch. ● Record the ammeter reading I. I = ............................................................... ● Open the switch. [1] R1R2(b) Use six different pairs of resistors to provide six different values of (R1 + R2). R1R2 1 For each arrangement, record R1, R2 and I in a table. Include values of and in (R1 + R2) I your table. [10] 1 R1R2(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] I (R1 + R2) (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] R1R2(d) (i) It is suggested that the quantities I and are related by the equation (R1 + R2) 1 R1R2 = P + Q I + [ (R1 R2)] where P and Q are constants. Using your answers to (c)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (ii) The constants P and Q are related to the electromotive force (e.m.f.) E of the power supply and the resistance Z of resistor Z by 1 Z P = and Q = . E E Determine the values of E and Z. Give appropriate units. E = ............................................................... Z = ............................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) 1(b) Six (or more) I values with different resistance pairings of R1, R2 without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc. 5 Range: 33Ω and 47Ω resistors used as a pair and 68Ω and 82Ω resistors used as a pair. 1 Column headings: Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention, e.g. 1 / I / A–1, 1 2 1 2 R R R R     +   / Ω. 1 Consistency: All values of I must be given to the nearest 0.1mA or all to the nearest 0.01mA. 1 Significant figures: All values of 1 2 1 2 R R R R     +   must be given to 2 s.f. or 3 s.f. 1 Calculation: Values of 1 / I and 1 2 1 2 R R R R     +   are correct. 1 Question Answer Marks 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 the x and y directions. Axes 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 in both x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ± 1 Ω on the 1 2 1 2 R R R R     +   axis of all plotted points. 1 1(c)(ii) Line of best fit: Judge by the 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. Line must not be kinked or thicker than half a small square. 1 Question Answer Marks 1(c)(iii) Gradient: 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. Method of calculation must be correct, e.g. Δy / Δx. Gradient sign on answer line matches graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph at 1 2 1 2 R R R R     +   = 0, accurate to half a small square. 1 1(d)(i) Value of P = candidate’s gradient and value of Q = candidate’s y-intercept. Values must not be written as fractions. 1 Unit for P is correct e.g. Ω–1A–1 or Ω–1 mA–1 or V–1 and unit for Q is correct e.g. A–1 or mA–1. 1 1(d)(ii) E and Z correctly calculated from P and Q using: E = 1 / P and Z = EQ or Z = Q / P and units for E (V) and Z (Ω) correct. 1

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2 In this experiment, you will investigate the time taken for filter papers to fall in air. (a) (i) ● You have been provided with filter papers of two different sizes. Take one sheet of the smaller filter paper. ● The diameter of one sheet of filter paper is d, as shown in Fig. 2.1. filter paper d Fig. 2.1 Measure and record d. d = ................................................... cm [2] (ii) Calculate the area A of the filter paper using πd2 A = . 4 A = ...................................................cm2 [1] (iii) Justify the number of significant figures that you have given for your value of A. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Set up the apparatus as shown in Fig. 2.2. six sheets of filter paper clamp boss stand metre rule bench Fig. 2.2 ● Hold the six sheets of the smaller filter paper at the top of the metre rule, as shown in Fig. 2.2. ● Release the filter papers and start the stop-watch. ● The time between release and the filter papers hitting the bench is t. Measure and record t. t = ...................................................... s [2] (ii) Estimate the percentage uncertainty in t. Show your working. percentage uncertainty = ......................................................... [1] (iii) Measure and record the total mass m of the sheets of smaller filter paper. m = .......................................................... [1] (c) (i) Repeat (a)(i) and (a)(ii) using one of the larger sheets of filter paper. d = ......................................................... cm A = ....................................................... cm2 [1] (ii) Using two sheets of the larger filter paper, repeat (b)(i) and (b)(iii). t = ............................................................ s m = ............................................................... [1]

Mark scheme: 2(a)(i) d = 11.0 ± 0.5cm. 1 Raw value(s) of d recorded to the nearest millimetre. 1 2(a)(ii) A calculated correctly. 1 2(a)(iii) Number of significant figures in A is linked to the number of significant figures in d. 1 2(b)(i) Value of t in the range 0.5 ⩽ t ⩽ 1.0s and given to 0.1s or better. 1 Repeated measurement of t. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty in the range 0.2–0.5 s. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to find percentage uncertainty. 1 2(b)(iii) Mass in the range 2.0–10.0g and measured to the nearest 0.1g or better and with unit. 1 2(c)(i) Second value of d. 1 2(c)(ii) Second value of t is larger than the first value of t. 1 2(d)(i) Two values of k calculated correctly. The final values must not be written as 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 Difficulty with filter paper at the start, e.g. paper not horizontal/paper too high to view against ruler/parallax in viewing start position/paper held by hand which moves/metre rule not vertical. C Difficult to start stop-watch and release filter paper at the same time. D Problem with fall of filter paper with a reason, e.g. paper does not fall vertically/erratic path/hits boss or stand/misses bench/papers separate while falling. E Difficulty with judging when to stop the stop-watch with a reason, e.g. difficult to align head at bench level/papers arrive separately. F Times are small so large error/uncertainty (in t) or high percentage uncertainty in t. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 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 Improved method to hold/release filter paper, e.g. horizontal bar level with top of rule or use a set square with detail, e.g. use set square between bench and ruler or use plumb-line. C Video/record/film with timer/frame-by-frame. D Use more filter papers/heavier or thicker paper/glue together or switch off air-conditioning/close windows/use a wind shield. E Use a pressure sensor below/position sensor above or below. F Use a greater distance to fall through or use larger diameters/use fewer papers/use lighter papers/use thinner papers (Credit once only if heavier papers suggested for D and lighter papers suggested for F.) 1 mark for each point up to a maximum of 4. 4

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