Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate an electrical circuit. (a) ● Connect the circuit shown in Fig. 1.1. 1.5 V d.c. a b S U T wire metre rule Q V P R component holder Fig. 1.1 ● S, T and U are crocodile clips. Connect one of the resistors labelled with its resistance in the component holder as resistor R, and record its resistance R. R = ............................................................... ● Close the switch. ● Place U on the wire and adjust its position so that the voltmeter indicates as near to zero as possible. ● The distance between S and U is a and the distance between U and T is b, as shown in Fig. 1.1. Measure and record a and b. a = ............................................................... b = ............................................................... ● Open the switch. [2] (b) Change R and determine a and b. Repeat until you have six sets of values of R, a and b. 1 b Record your results in a table. Include values of and in your table. R a [10] b 1(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] a 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 b, a and R are related by the equation b M = + N a R where M and N are constants. Using your answers in (c)(iii), determine the values of M and N. Give appropriate units. M = ............................................................... N = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value for R with unit. 1 Value for a with unit in range 10.0–75.0 cm. 1 1(b) Six (or more) sets of readings of R (different values) and a and b with correct trend (as R increases, a increases and b 5 decreases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc. Range: R values include 220  and 4700 . 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) and b / a (no unit) Consistency: Values of a and b must all be given to the nearest 0.1 cm. 1 Significant figures: 1 All values of b / a must be given to the same number of s.f. as (or one more than) the lowest number of s.f. in the corresponding a and b values. Calculation: Values of 1 / R are 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 positive. All points in the table must be plotted (at least 5). It must be possible to draw a straight line that is within ± 0.2 on the b / a 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 M = candidate’s gradient and value of N = candidate’s y-intercept. 1 The values must not be written as fractions or given to only one significant figure. Unit for M correct (e.g. ) and no unit for N. 1

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2 In this experiment, you will investigate the path of a jet of water. (a) ● Assemble the apparatus as shown in Fig. 2.1. clamp boss bottle stand paper strip stand hole ≈ 14 cm boss G-clamp rod of clamp ≈ 27 cm ≈ 17 cm tray bench Fig. 2.1 (not to scale) ● Adjust the heights of the bosses so that the bottom of the bottle is approximately 27 cm above the tray and the rod of the clamp is approximately 17 cm above the tray. ● Move the stands so that the horizontal distance from the hole in the bottle to the rod of the clamp is approximately 14 cm, as shown in Fig. 2.1. ● The height of the centre of the hole above the tray is A. The distance from the centre of the hole to the centre of the rod is B. The height of the rod above the tray is C, as shown in Fig. 2.2. B A C Fig. 2.2 Measure and record A, B and C. A = ......................................................... cm B = ......................................................... cm C = ......................................................... cm ● Calculate s using s = A - C. s = ......................................................... cm ● Calculate x using 2 2 x = (B - s ) . x = ......................................................... cm [3] (b) (i) ● Position the empty jug under the rod. ● Add water to the bottle until there is a jet of water passing over the rod, as shown in Fig. 2.3. water level jet of water jug Fig. 2.3 ● As the water level falls, the jet will get closer to the rod. When the jet touches the rod, mark the water level on the paper strip, as shown in Fig. 2.4. mark h paper strip Fig. 2.4

Mark scheme: 2(a) Values for A, B and C. 1 B in range 16.0–24.0 cm. 1 Correct calculation of x. 1 2(b)(i) Value(s) of h, with unit, to nearest mm. 1 Evidence of repeat readings of h. 1 2(b)(ii) Percentage uncertainty in h based on an absolute uncertainty in the range 0.2–0.8 cm. 1 Correct method of calculation to obtain percentage uncertainty, e.g. (absolute uncertainty  100 / final value from (b)(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) Second set of values for A and B. 1 Second value for h. 1 Second value of h less than first value of h. 1 2(d)(i) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(d)(ii) Justification for significant figures in k linked to significant figures in x, h and s. 1 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 20% leading to a consistent conclusion. 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty when measuring B with reason e.g. difficult to judge centre of rod or difficult to align hole with ruler. C Difficulty when measuring A or C with reason e.g. parallax error, difficult to hold/maintain ruler vertical. D Difficulty with water jet with a description e.g. too thick, multiple streams, jet spreads out. E Difficulty with judging/marking water level because of needing to look at the rod and water at the same time or water level is (quickly) changing. F Difficult to see/mark/judge water level with reason e.g. water is colourless/ribbed bottle. G Difficulty with paper strip e.g. ink on strip can be washed away. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings (for different values of h) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B Use string or measuring tape or use a thinner rod or use rule(r) with scale starting at end or measure horizontal distance and vertical distance and calculate a value for B. C Improved method to ensure vertical e.g. use clamped ruler/plumb line/spirit level. D Decrease diameter of hole or use a hole with smoother edge. E Improved method to determine water level e.g. record/film/video with scale/ruler in view or put cap/cork on bottle top or cover hole at moment jet hits rod. F Use coloured water/smooth bottle. G Use permanent marker/waterproof strip. 1 mark for each point up to a maximum of 4.

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