Cambridge A Level Physics 9702 — 2022 May/June Paper 5 · Variant 2

1 Two parallel cylindrical conductors each have a small cross‑sectional area A. A thin metal bar connects the two conductors, as shown in Fig. 1.1. L area A C cylindrical x conductors metal bar C y area A Fig. 1.1 (not to scale) The metal bar has a square cross‑section with sides of length y. For each conductor, the distance between its end C and the centre of the metal bar is L. The distance between the centres of the conductors is x. The ends C are connected to a power supply and the current I in the conductors is measured. It is suggested that I is related to L by the relationship E 2PL Qx = + 2 I A y where E is the electromotive force (e.m.f.) of the power supply, and P and Q are constants. Plan a laboratory experiment to test the relationship between I and L. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for P and Q. In your plan you should include: ● the procedure to be followed ● the measurements to be taken ● the control of variables ● the analysis of the data ● any safety precautions to be taken. 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[15]

Mark scheme: 1 Defining the problem L is the independent variable and I is the dependent variable or vary L and measure I 1 keep E constant 1 Methods of data collection labelled diagram of workable experiment including:  circuit diagram with power supply connected to ends C  ammeter in series with power supply and conductors  correct symbol for ammeter and power supply 1 circuit diagram with voltmeter correctly positioned to measure E across the power supply 1 use a rule(r) to measure L and x 1 use a micrometer/calipers to measure y 1 Question Answer Marks 1 Method of analysis plot a graph of 1 I against L or equivalent (e.g. L against 1 I ) (Do not accept log graphs.) 1 gradient 2 AE P   (for L against 1 I : 2 gradient AE P   ) 1 2 -intercept y Ey Q x   (for L against 1 I : 2 -intercept 2 y Py Q Ax   or 2 -intercept gradient y Ey Q x    ) 1 Question Answer Marks 1 Additional detail including safety considerations 6 D1 do not touch/use (heat resistant) gloves to avoid hot conductors/metal bar or use a protective resistor/small e.m.f. to reduce the current or switch off when not in use/when moving bar D2 keep A and y constant D3 keep x constant D4 use of micrometer/calipers to measure diameter of conductor and A = d2 / 4. D5 repeat measurements of diameter along conductors/different (perpendicular) directions/different points and average or repeat measurements of y in different (perpendicular) directions/different points/along bar and average D6 method to ensure that L is the same for each conductor, e.g. check both lengths D7 method to determine L e.g. measure to edge and add y / 2 or method to determine x e.g. measure between the conductors and add diameter D8 method to keep x constant with reason, e.g. adhesive/plasticine/blocks (one either side of each conductor) to prevent cylindrical conductors from moving D9 method of ensuring good electrical contact, e.g. clean metal bar/cylindrical conductors or use of solder or crocodile clips to connect circuit to the conductors D10 relationship valid if a straight line is produced (not passing through the origin)

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2 The brightness of some stars varies regularly. These stars are called variable stars. Fig. 2.1 shows the variation of luminosity with time for a variable star. period luminosity time Fig. 2.1 A student determines the period T and mean luminosity L of the star. The student repeats the process for different variable stars. It is suggested that L and T are related by the equation L = SKT a where S is the luminosity of the Sun, and a and K are constants. (a) A graph is plotted of lg L on the y‑axis against lg T on the x‑axis. Determine expressions for the gradient and y‑intercept. gradient = ............................................................... y‑intercept = ............................................................... [1] (b) Values of T and L are given in Table 2.1. Table 2.1 T / days L / 1030 W lg (T / days) lg (L / 1030 W) 22 2.9 ± 0.2 32 4.9 ± 0.2 42 6.9 ± 0.2 54 9.8 ± 0.2 78 16 ± 2 97 21 ± 2 Calculate and record values of lg (T / days) and lg (L / 1030 W) in Table 2.1. Include the absolute uncertainties in lg (L / 1030 W). [2] (c) (i) Plot a graph of lg (L / 1030 W) against lg (T / days). Include error bars for lg (L / 1030 W). [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) y-intercept = lgSK 1 2(b) lg (T / days) lg (L / 1030 W) 1.34 or 1.342 0.46 or 0.462  0.03 1.51 or 1.505 0.69 or 0.690  0.02 1.62 or 1.623 0.84 or 0.839  0.01 1.73 or 1.732 0.99 or 0.991  0.01 1.89 or 1.892 1.20 or 1.204  0.05 or 0.06 1.99 or 1.987 1.32 or 1.322  0.04 Values of lg (T / days) and lg (L / 1030 W) correct as shown above. 1 Absolute uncertainties in lg (L / 1030 W) correct as shown above. 1 2(c)(i) Six points from (b) plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in lg (L / 1030 W) plotted correctly. All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Straight line of best fit drawn. Points must be balanced. Do not accept line from top point to bottom point. Line must pass between (1.43, 0.60) and (1.45, 0.60) and between (1.84, 1.15) and (1.86, 1.15). 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted. 1 Question Answer Marks 2(c)(iii) Gradient determined with clear substitution of data points into y / x. Distance between data points must be greater than half the length of the drawn line. 1 Gradient of worst acceptable line determined. uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(c)(iv) y-intercept determined by substitution into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) Do not allow methods using a false origin. 1 Question Answer Marks 2(d) a = gradient = (c)(iii) and a and K both given to two or three significant figures. 1 Value of K determined using y-intercept. Correct method must be seen. -intercept 30 30 26 10 10 10 10 3.85 10 y K S      (c)(iv) or -intercept lg 30 10 10 y S K    or 26 lg 3.85 10 30 10 10 K     (c)(iv) 1 absolute uncertainty in a = absolute uncertainty in gradient and   -intercept WAL -intercept 30 10 10 10 y y K S     Correct substitution of numbers must be seen. 1 2(e) L determined from (d) or (c)(iii) and (c)(iv) with correct substitution and correct power of ten(s). Do not accept incorrect POT for a or K. L = 3.85  1026  (d)  5.0(c)(iii) or lg lg5.0 -intercept L y    (c)(iii) 1

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