Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate an electrical circuit. (a) • Place the 15 Ω resistor in component holder P. • Place the 22 Ω resistor in component holder Q. • Set up the circuit shown in Fig. 1.1. y metre rule wire A K L P Q Fig. 1.1 • K and L are crocodile clips. The resistors in the component holders have resistances P and Q. Place L approximately half-way along the wire. • The distance between K and L is y as shown in Fig. 1.1. Record P, Q and y. P = ............................................................... Q = ............................................................... y = ............................................................... • Close the switch. • Record the ammeter reading I. I = .............................................................. • Open the switch. [1] (b) • Change one or both of the resistors in P and Q. • Record the new values of P and Q. P = ............................................................... Q = ............................................................... • Close the switch. • Change the position of L on the wire so that the ammeter reading is as close as possible to the value for I in (a). • Record y. y = ............................................................... • Open the switch. [1] (c) Repeat (b) until you have six sets of readings of P, Q and y. Include your readings from (a) and (b). PQ Record your results in a table. Include values of in your table. P + Q [9] PQ(d) (i) Plot a graph of y on the y-axis against on the x-axis. [3] P + Q (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) It is suggested that the quantities y, P and Q are related by the equation MPQ y = – + N P + Q where M and N are constants. Using your answers in (d)(iii), determine values for M and N. Give appropriate units. M = .............................................................. N = ............................................................... [2] (f) Theory suggests that N E = M I where E is the electromotive force (e.m.f.) of the cell. Calculate E. Give an appropriate unit. E = ...........................................................[1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) 1 1(b) Value of y with unit and in the range 20.0–75.0 cm. 1 1(c) Six sets of readings of P, Q (different pairs) and y without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: Resistor values include the pair (15 Ω and 12 Ω) and the pair (27 Ω and 22 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. y / m and PQ / (P + Q) / Ω. 1 Consistency: All values of y must be given to the nearest mm only. 1 Significant figures: Values of PQ / (P + Q) must be given to 2 or 3 significant figures. 1 Calculation: Values of PQ / (P + Q) are correct. 1 1(d)(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 (no “blobs”). Points must be plotted to an accuracy of half a small square. 1 Quality: General trend of points on graph must be negative. All points in the table (at least 5) must be plotted on the grid. It must be possible to draw a straight line that is within ±0.050 m (to scale) on the y-axis of all plotted points. 1 Question Answer Marks 1(d)(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 by the candidate (i.e. circled or labelled). Line must not be kinked or thicker than half a small square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient on answer line must match graph. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph with read-off at x = 0, accurate to half a small square. 1 1(e) Value of M = –candidate’s gradient and value of N = candidate’s intercept. The values must not be fractions. 1 Units for M (e.g. m Ω–1 or cm Ω–1 or mm Ω–1) and N (e.g. m or cm or mm) correct. 1 1(f) Correct calculation of E with unit. 1

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2 In this experiment, you will investigate the equilibrium of a system of three identical springs. (a) You have been provided with three springs attached to a ring. Measure and record the unstretched length S of the coiled section of one of the springs, as shown in Fig. 2.1. S Fig. 2.1 S = ...........................................................[1] (b) (i) • Set up the apparatus as shown in Fig. 2.2. rods of clamps bosses 90° spring springs mass hanger ring mass m stands bench Fig. 2.2 • The total mass m of the mass hanger and the slotted masses should be 0.300 kg. • Adjust the position of the bosses so that the centres of the rods of the clamps are at the same height above the bench. • Change the separation of the stands until the angle between the springs is 90°. • The lengths S1 and S2 of the coiled sections of the two springs attached to the ring are shown in Fig. 2.3. The angle between the single spring and the vertical is θ. θ S1 S2 Fig. 2.3 Measure and record m, S1, S2 and θ. m = .......................................................... kg S1 = ............................................................... S2 = ............................................................... θ = ............................................................. ° [2] (ii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ...........................................................[1]

Mark scheme: 2(a) 1 2(b)(i) Values of S1 and S2 and S1 > S2. 1 Value of raw θ to the nearest degree and value of θ < 45° on answer line. 1 2(b)(ii) Percentage uncertainty in θ based on an absolute uncertainty of 3–10°. 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 2(b)(iii) Correct calculation of e1 cosθ and e2 sinθ. 1 2(b)(iv) Justification for significant figures in e1 cosθ linked to s.f. in: (S1 – S) and θ or e1 and θ or S, S1 and θ. 1 2(c) Second values of S1 and S2. 1 Quality: Second values of S1 and S2 greater than first values of S1 and S2. 1 Second value of θ. 1 2(d)(i) Two values of β calculated correctly. 1 2(d)(ii) Valid comment consistent with the calculated values of β, testing against a criterion stated by the candidate. 1 2(e) Correct calculation of k using second value of β with a correct unit. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to judge the vertical. C Difficult to determine θ/angle because of parallax error or cannot see the lines defining the angle. D Difficult to determine θ/angle because cannot hold the protractor steady. E Difficult to measure S1 or S2 with reason e.g. springs move or mass moves. F The stands tilt/topple/slide or the bosses twist on loading. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take many readings (for different values of m) and plot a graph or take more values of β and compare (not “repeat readings” on its own). B Method to get vertical reference e.g. plumb line/use of set square on bench with metre rule/use spirit level vertically. C Use a larger protractor/have a protractor drawn on card at the back/use projection ideas/take a photograph and measure angle. D Clamp protractor (valid method). E Clamp ruler/take photograph with scale or ruler in the frame. F Use G-clamps/clamp the stands/use heavy weights/lower the bosses. 1 mark for each point up to a maximum of 4. 4

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