Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate an electrical circuit. (a) ● Connect the circuit shown in Fig. 1.1. 3.0 V d.c. 1.5 V d.c. + + + V X Y component holder Fig. 1.1 ● Ensure that the polarities of the two power supplies and the voltmeter are as shown in Fig. 1.1. ● Connect one of the labelled resistors into the component holder as resistor Y, as shown in Fig. 1.1. Record the resistance R of resistor Y. R = ............................................................... ● The voltmeter reading should be approximately 3 V. Record the voltmeter reading V. V = ............................................................... [2] (b) Change Y and record R and V. Repeat until you have six sets of values of R and V. 1 Record your results in a table. Include values of in your table. R [10] 1 (c) (i) Plot a graph of V on the y-axis against on the x-axis. [3] R (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 V and R are related by the equation a V = + b R where a and b are constants. Using your answers in (c)(iii), determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value for R in range 0.68–4.7 k with unit. 1 Value for V in range 2.30–3.50 V with unit. 1 1(b) Six sets of readings of R and V with correct trend (as V increases as R increases) and without help from the Supervisor 5 scores 5 marks, five sets scores 4 marks, etc. Range: Rmin = 0.68 k and Rmax = 4.7 k. 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1 / R (k–1). Consistency: 1 Values of V must all be given to the nearest 0.01 V. Significant figures: 1 Values of 1 / R should be given to the same number of s.f. as, or one more than, the number of s.f. in the corresponding value of R. Calculation: Values of 1 / R calculated correctly. 1 1(c)(i) Axes: 1 Axes must be labelled with the correct quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used. Scales must not be awkward (e.g. 3:10 or fractions). 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. Points must be plotted to an accuracy of half a small square in both x and y directions. Quality: 1 Trend of points must be negative. All points in the table (at least 5) must be plotted. It must be possible to draw a straight line that is within  0.01 V on the V axis of all plotted points. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least 5 points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 1 The hypotenuse of the triangle used should 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, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at 1 / R = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(d) Value of a = candidate’s gradient and value of b = candidate’s y-intercept. 1 The values must not be written as fractions or given to only one significant figure. Units for a (e.g. k V) and b (e.g. V) are correct. 1

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2 In this experiment, you will investigate the properties of linked rubber bands. You are provided with two elastic strings made from linked rubber bands. The longer one is made from three rubber bands and the shorter one is made from two rubber bands. Each string has a 50 g mass attached to one end. (a) Measure and record the unstretched length l 0 of the longer elastic string, as shown in Fig. 2.1. l0 Fig. 2.1 l 0 = ................................................... cm [1] (b) ● Assemble the apparatus as shown in Fig. 2.2 using the longer elastic string and with the clip approximately 40 cm above the pad of paper. rod of clamp elastic string boss stand clip 100 g mass 50 g mass ≈ 40 cm d bench pad of paper Fig. 2.2 ● The distance between the bottom of the 50 g mass and the pad is d. Adjust the boss until d is approximately 2 cm. ● Measure and record d. d = ........................................................ cm ● Remove the 100 g mass from the elastic string, as shown in Fig. 2.3. pad d0 Fig. 2.3 ● Measure and record the distance d0 between the bottom of the 50 g mass and the pad. d0 = ........................................................ cm [2] (c) (i) ● Using your hand, raise the 50 g mass until the bottom of the mass is level with the bottom of the clip, as shown in Fig. 2.4. clip h Fig. 2.4 ● Release the mass and watch (and listen) to see if it just touches the pad. If it doesn’t just touch the pad, change the position of the clip and repeat the process. Continue until the mass just touches the pad. ● Measure and record the vertical height h of the bottom of the clip above the pad, as shown in Fig. 2.4. h = ................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of h. Show your working. percentage uncertainty = ..................................................... % [1] (iii) ● Using your hand, pull the 50 g mass down until it is just touching the pad, as shown in Fig. 2.5. lmax Fig. 2.5 ● Measure and record the length l max of the elastic string, as shown in Fig. 2.5. l max = ................................................... cm [1]

Mark scheme: 2(a) Value for l0 in range 30.0–50.0 cm. 1 2(b) Value(s) for d to nearest mm. 1 Final d in range 1.0–3.0 cm. 1 2(c)(i) Value for h. 1 2(c)(ii) Percentage uncertainty in h based on an absolute uncertainty in the range 0.3–0.5 cm. 1 Correct method of calculation to obtain percentage uncertainty, e.g. (absolute uncertainty  100 / final value from (c)(i)). If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is shown clearly. 2(c)(iii) Value for lmax to nearest mm and greater than l0. 1 2(d) Second values of d0 and d. 1 Second values of l0, h and lmax. 1 Second value of h less than first value of h. 1 2(e)(i) Two values of C calculated correctly. 1 The final C values must not be written as fractions of given to only one significant figure. 2(e)(ii) Justification for significant figures in C based on the significant figures in (lmax – l0), h and (d0 – d). 1 2(f) Calculation of percentage difference between candidate’s two C values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficult to measure l 0 with a reason e.g. hard to get the string straight / hard not to stretch the string. C Difficult to measure d with a reason e.g. parallax or 100 g mass falls off or rule moves string. D Hard to judge if the mass just touches the pad or difficult to align mass with clip before release. E Parallax error when measuring h. F Difficult to measure lmax with a reason e.g. rule unsteady or string may not be vertical. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings and plot a graph or take more readings and compare C values (not “repeat readings” on its own). 4 B Improved method to find l0 e.g. method to fix one end (e.g. tape to the bench). C Use smaller 100 g mass or mirror scale behind 50 g mass. D Improved method for judging contact e.g. video and replay frame by frame or use pressure pad or use sand tray or place microphone near paper and display trace on CRO. E Clamp rule and use pointer (for h or d). F Measure to bottom of mass (or to paper pad) and subtract diameter of mass (for lmax). 1 mark for each point up to a maximum of 4.

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