Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 5 · Variant 1

1 Two coils, C and D, are placed with their axes on a straight line, as shown in Fig. 1.1. R coil D coil C Fig. 1.1 A resistor of resistance R is connected in series with coil C. A changing magnetic flux of frequency f in coil C causes an electromotive force (e.m.f.) E to be induced across the terminals of coil D. It is suggested that E is related to f by the relationship pf qV E = R where V is the potential difference across the resistor and coil C, and p and q are constants. Plan a laboratory experiment to test the relationship between E and f. 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: Question Answer Marks 1 Defining the problem. f is the independent variable and E is the dependent variable or vary f and measure E 1 keep V and R constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • coils C and D placed with their axes on a straight line • separate workable circuit for coil D • (a.c.) voltmeter or oscilloscope connected across coil D (Do not accept a power supply connected to coil D.) a.c. power supply/signal generator connected to coil C 1 workable circuit for coil C with power supply and (a.c.) voltmeter/oscilloscope in parallel with resistor and coil C 1 method to determine f, e.g. read from signal generator or use of oscilloscope 1 Method of Analysis plot a graph of lg E against lg f or equivalent (e.g. ln E against ln f) 1 q = gradient 1 R -intercept 1 p =  10y V R -intercept (for ln E against ln f: p =  ey ) V 1 Additional detail including safety considerations 6 D1 precaution (to prevent burns) from hot coils/hot resistor, e.g. use gloves to handle hot coil/resistor, switch off circuit and wait for hot coil/resistor to cool D2 keep the number of turns on each coil constant D3 keep distance between the coils constant D4 workable circuit diagram to determine R. e.g. circuit with ammeter connected in series and voltmeter in parallel with resistor or resistor connected to ohmmeter only D5 determination of resistance R: potential difference across R ÷ current in R or use ohmmeter to measure R D6 method to keep distance between the coils constant, e.g. fix/clamp coils to bench D7 method to determine f from oscilloscope, e.g. period T = time-base  horizontal distance and f = 1 / T D8 method to determine V or E from oscilloscope, e.g. V or E = y-gain  vertical distance D9 method to increase E e.g. use iron core, place coils closer, increase V, decrease R  pV  D10 relationship valid if a straight line is produced (passing through log )    R  Do not accept line passing through the origin.

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2 A block of modelling clay of mass M is attached to a string as shown in Fig. 2.1. string block pellet h pellet Fig. 2.1 A pellet travelling at speed u enters the block and causes the block to move through a vertical height h. The experiment is repeated for different values of M. It is suggested that h and M are related by the equation 1 M + Z 2 = 2 g h c uZ m where g is the acceleration of free fall and Z is a constant. 1 (a) A graph is plotted of on the y-axis against M on the x-axis. h Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of M and h are given in Table 2.1. Table 2.1 1 1 - M / g h / cm / cm 2 h 565 21.0 ± 0.2 637 17.8 ± 0.2 675 16.2 ± 0.2 723 14.6 ± 0.2 790 12.6 ± 0.2 892 10.2 ± 0.2 1 1 - Calculate and record values of / cm 2 in Table 2.1. h 1 Include the absolute uncertainties in . [2] h 1 1 - 2 against M / g.(c) (i) Plot a graph of / cm h 1 Include error bars for . [2] h (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) 2g 1 gradient = uZ 2g y-intercept = u 2(b) 1 −1 1 2 / cm h 0.218 or 0.2182 0.237 or 0.2370 0.248 or 0.2485 0.262 or 0.2617 0.282 or 0.2817 0.313 or 0.3131 Values correct as shown above. 1 1 Uncertainties in from ± 0.001 to ± 0.003. h 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. 1 1 Error bars in plotted correctly. h All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Do not accept line from top point to bottom point. Points must be balanced. Line must pass between (605, 0.230) and (615, 0.230) and between (845, 0.300) and (855, 0.300) Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1 All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient determined of worst acceptable line. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point with consistent power of ten into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. 1 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 accept ECF from false origin method. 2(d)(i) u determined using y-intercept and u and Z given to 2, 3 or 4 significant figures. 1 2  981 44.29 u = = y -intercept (c)(iv) Z determined using gradient with method shown and u and Z given with SI units with appropriate powers of ten. 1 2  981 44.29 y -intercept (c)(iv) Z = = or Z = = u  gradient u (c)(iii) gradient (c)(iii) 2(d)(ii) Percentage uncertainty in Z with method shown. 1  y -intercept gradient  percentage uncertainty in Z =  +   100  y -intercept gradient  or Correct substitution for u and  u gradient  percentage uncertainty in Z =  +   100  u gradient  or Correct substitution for max/min methods. 2(e) M determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d)(i) with correct substitution. 1  1  − y -intercept    25  M = gradient or uZ uZ M = − Z = − Z 2gh 221.5

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