Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will determine the resistivity of a metal. (a) ● Set up the circuit shown in Fig. 1.1. V Fig. 1.1 ● The voltmeter reading is E. Record E. E = ........................................................... V ● Set up the circuit shown in Fig. 1.2. wire nail nail A R1 R2 nail Fig. 1.2 (not to scale) ● You have been provided with several resistors, each with a different value of resistance. Select resistors and connect them so that R1 = 33 Ω and R2 = 56 Ω. ● Record R1 and R2. R1 = ............................................................... R2 = ............................................................... ● Calculate (R1 + R2). (R1 + R2) = ............................................................... ● Close the switch. ● The ammeter reading is I. Record I. I = ......................................................... mA ● Open the switch. [1] (b) Change the values of R1 and R2 to provide six different values of (R1 + R2). For each arrangement, record values of R1, R2 and I in a table. Include values of (R1 + R2) 1 and in your table. I [8] 1(c) (i) Plot a graph of on the y-axis against (R1 + R2) 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, R1 and R2 are related by the equation 1 = F(R1 + R2) + G I where F and G are constants. Using your answers in (c)(iii), determine the values of F and G. Give appropriate units. F = ............................................................... G = ............................................................... [2] (e) (i) Use the micrometer to measure the diameter d of the wire. d = ......................................................... [2] (ii) It is suggested that G is given by the equation 4ρL G = πd2E where L is 0.560 m and ρ is the resistivity of the metal of the wire. Using your answers in (a), (d) and (e)(i), determine a value for ρ. ρ = .................................................. Ω m [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Final value of E in the range 2.50–6.00 V. 1 1(b) Six (or more) sets of readings of R1 and R2 (different values of (R1 + R2)) and I with the correct trend (as (R1 + R2) 3 increases, I decreases) and without help from the Supervisor scores 3 marks, five sets scores 2 marks, etc. Range: Uses (R1 + R2) = 45  and (R1 + R2) = 138 . 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate. 1 The presentation of quantity and unit must conform to accepted scientific convention e.g. (R1 + R2) / , (A–1). Do not I allow 1 / I (A). Consistency: All raw values of I must be given to 0.1 mA or all given to 0.01 mA. 1 1 1 Significant figures: All values of must be given to the same number of s.f. as (or one more than) the number of s.f. in raw I I values. 1 1 Calculation: Values of are correct. I 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 on the grid (at least 5). It must be possible to draw a straight line that is within  4  on the (R1 + R2) 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 (R1 + R2) = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line is 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 F = candidate’s gradient and value of G = candidate’s y-intercept. 1 The values must not be written as fractions or given to only one significant figure. Correct unit for F e.g. mA–1 –1 1 and correct unit for G e.g. mA–1. 1(e)(i) All raw values given to either 0.01 mm or all to 0.001 mm 1 and final value of d in the range 0.100–0.300 mm with unit. Measurements of d repeated. 1 1(e)(ii) Correct calculation of using = d2EG / 4L. 1

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2 In this experiment, you will investigate the movement of a mass hanger. (a) You are provided with a number of paper clips. Use the top-pan balance to determine the mass m of one paper clip. m = ....................................................... g [1] (b) (i) ● Set up the apparatus as shown in Fig. 2.1. pulley mass hanger boss string adhesive stand putty h slotted mass bench Fig. 2.1 (not to scale) ● Lower the slotted mass until it just touches the bench. ● The distance between the bottom of the mass hanger and the bench is h, as shown in Fig. 2.1. Measure and record h. h = .................................................... cm [1] (ii) ● Add just enough paper clips to the mass hanger so that it falls smoothly to the bench without stopping. ● Record the total number N of paper clips on the mass hanger. N = ......................................................... [1] (iii) ● Adjust the position of the slotted mass so that it is just touching the bench again. ● Release the slotted mass and measure the time t for the mass hanger and N paper clips to fall to the bench. t = ......................................................... [2] (iv) Estimate the percentage uncertainty in your value of t. Show your working. percentage uncertainty = ..................................................... % [1] (v) The acceleration a of the mass hanger is given by the relationship 2h a = . t 2 Calculate a. a = ............................................... cm s–2 [1] (vi) Justify the number of significant figures that you have given for your value of a. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (c) ● Add two more paper clips to the mass hanger. ● Record the total number N of paper clips on the mass hanger. N = ............................................................... ● Repeat (b)(iii) and (b)(v). t = ............................................................... a = .................................................... cm s–2 [2] (d) It is suggested that the relationship between a, m and N is k 2Z = 1 + a Nm where Z is the mass of the slotted mass and has the value 10.0 g, and k is a constant. Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1]

Mark scheme: 2(a) Evidence of mass of 5 or more paper clips measured to the nearest 0.1 g or better 1 and mass of one paper clip determined. 2(b)(i) Raw h recorded to the nearest millimetre and final value of h in range 10.0–60.0 cm. 1 2(b)(ii) N recorded. 1 2(b)(iii) Value of t in the range 0.50–10.00 s with unit. 1 Evidence of repeats. 1 2(b)(iv) Percentage uncertainty based on an absolute uncertainty in t in the range 0.2–0.5 s. 1 Correct method of calculation to find percentage uncertainty e.g. absolute uncertainty  100 / value from (b)(iii). If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is shown clearly. 2(b)(v) Value of a calculated correctly. 1 2(b)(vi) Justification for significant figures in a linked to significant figures in h and t. 1 2(c) Second values of N and t. 1 Second value of t is smaller than the first value of t. 1 2(d) 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(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 25% 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 Difficult to measure h with a reason e.g. because mass hanger is not horizontal or rule not vertical or rule disturbs mass hanger/pulley. C t is small so uncertainty is large or large percentage uncertainty in t. D Difficult to measure t with a reason e.g. difficult to start stop-watch and release mass at the same time. E Difficulty with pulley and/or string e.g. hanger starts and stops or pulley too narrow so masses collide or masses too wide so collide. F Difficulty with adhesive putty e.g. mass of putty not taken into account or adhesive putty adds mass to slotted mass. G Difficulty with paper clips e.g. paper clips fall off mass hanger or difficult to balance clips on hanger or paper clips are discrete (large increments) so mass hanger suddenly releases and falls. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings (for different values of N) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B Workable method to measure h accurately e.g. clamp metre rule (and use a fiducial marker). C Use a longer string or larger h. D Workable method to measure t e.g. record/film/video with timer in view/frame by frame or electromagnet for start, gate for end with timer or motion sensor above or below. E Workable improvement e.g. use a pulley with larger diameter or masses of smaller diameter. F Valid method to account for the mass of the adhesive putty e.g. measure mass and add on or tie mass using string or use tape. G Workable method for improvement e.g. hook/container added to hanger or use smaller/lighter paper clips. 1 mark for each point up to a maximum of 4.

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