Cambridge A Level Physics 9702 — 2021 May/June Paper 5 · Variant 2

1 A student investigates the heating of a solid metal cylinder. Fig. 1.1 shows the cylinder of cross‑sectional area A and height h. A h cylinder Fig. 1.1 The student places the cylinder and an electrical heater in a beaker of water. The electrical heater is switched on and the student measures the time t for the temperature of the water to increase by Δθ. A number of cylinders of the same material but with different cross‑sectional areas are available. It is suggested that the relationship between t and A is Pt = AhWΔθ + ZΔθ where P is the power of the heater and W and Z are constants. Design a laboratory experiment to test the relationship between t and A. Explain how your results could be used to determine values for W and Z. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: ● 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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Mark scheme: 1 Defining the problem A is the independent variable and t is the dependent variable or vary A and measure t 1 keep Δθ constant 1 Methods of data collection labelled diagram of workable experiment including: • beaker of water • cylinder in water • electrical heater in water • thermometer in water • minimum of three labels from heater, thermometer, cylinder, water, beaker 1 circuit diagram to determine power of the heater e.g. ammeter and voltmeter correctly positioned with a power supply or wattmeter correctly connected to power supply and heater 1 method to determine time for temperature of water to increase or t, e.g. use a stopwatch/timer 1 method to determine A, e.g. micrometer/calipers to determine diameter of cylinder and A = πd2 / 4 1 Method of analysis plot a graph of t against A (not logarithmic graphs) 1 gradient P W h θ × = Δ 1 -intercept y P Z θ × = Δ 1 Question Answer Marks 1 Additional detail including safety considerations 6 D1 wear (heat proof) gloves to prevent burns from hot beaker/cylinder/heater/water D2 keep P and h constant D3 check that/ensure/keep initial temperature of the water constant or volume/mass of water constant D4 use calipers/ruler to measure h D5 repeat measurements of diameter in different directions/at different positions along cylinder and average D6 method to calculate power of heater e.g. P = VI linked to correct circuit diagram for ammeter/voltmeter method D7 repeat measurements of t for same A and average t D8 ensure heater and cylinder are (totally) submerged/immersed or stir water (using a glass rod/stirrer) D9 relationship valid if a straight line (not passing through the origin) D10 method to insulate beaker, e.g. use of a lid on the beaker or foam/insulation around outside of beaker

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2 A student investigates the current in a circuit containing a cell, as shown in Fig. 2.1. E r A R1 R2 P Q Fig. 2.1 The student connects two resistors of resistances R1 and R2 between P and Q. The ammeter measures the current I. The student repeats the experiment with different resistors between P and Q. It is suggested that I, R1 and R2 are related by the equation E = I(R1 + R2 + r) where E is the electromotive force (e.m.f.) and r is the internal resistance of the cell. 1 (a) A graph is plotted of on the y‑axis against (R1 + R2) on the x‑axis. I Determine expressions for the gradient and y‑intercept. gradient = ............................................................... y‑intercept = ............................................................... [1] (b) Values of R1, R2 and I are given in Table 2.1. Each resistance value has a percentage uncertainty of ± 5%. Table 2.1 1R1 / Ω R2 / Ω (R1 + R2) / Ω I / mA / A–1 I 22 33 17.2 22 47 14.2 22 56 12.8 33 47 12.4 33 56 11.4 47 56 10.1 1 Calculate and record values of (R1 + R2) / Ω and / A–1 in Table 2.1. I Include the absolute uncertainties in (R1 + R2). [2] 1(c) (i) Plot a graph of / A–1 against (R1 + R2) / Ω. I Include error bars for (R1 + R2). [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) gradient = 1 E y-intercept = r E 1 2(b) (R1 + R2) / Ω 1 I / A–1 55 58.1 or 58.14 69 70.4 or 70.42 78 78.1 or 78.13 80 80.6 or 80.65 89 87.7 or 87.72 103 99.0 or 99.01 Values of (R1 + R2) and 1 I as shown above. 1 Absolute uncertainties in (R1 + R2) from ± (2.75 or 2.8 or 3) to ± (5.15 or 5.2 or 5). 1 2(c)(i) Six points plotted correctly. Must be accurate to the nearest half a small square. Diameter of points must be less than half a small square. 1 Error bars in (R1 + R2) 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 Question Answer Marks 2(c)(ii) Line of best fit drawn covers all points. Points must be balanced. Do not allow line from top point to bottom point. Line must pass between (61.0, 65.0) and (63.5, 65.0) and between (96.5, 95.0) and (98.5, 95.0). 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all error bars). All error bars must be plotted. 1 2(c)(iii) Gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least 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 of correct point 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 ECF from false origin method. 1 2(d)(i) E determined using gradient and E and r given to two or three significant figures. 1 gradient E = 1 r determined using y-intercept with correct substitution and units with correct power of ten for E and r. r = y-intercept / gradient or r = E × y-intercept 1 Question Answer Marks 2(d)(ii) Absolute uncertainty in E determined with method shown e.g. gradient gradient E E Δ Δ = × or correct substitution for max/min methods e.g. 1 min gradient E E Δ = − 1 max gradient E E Δ = − 1 2(e) Value of R2 determined from (d)(i) or (c)(iii) and (c)(iv), with correct substitution and correct power of ten. ( ) 2 22 0.0075 E R r = − + or ( ) 2 1 22 0.0075 gradient R r = − + × 1

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