Cambridge A Level Physics 9702 — 2022 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate an electrical circuit. (a) (i) You have been provided with a stand with two clamps attached. Do not change the positions of the clamps during the experiment. Measure the distance x between the centres of the rods of the two clamps, as shown in Fig. 1.1. rod of clamp x rod of clamp Fig. 1.1 x = .................................................... cm [1] (ii) You have been provided with a length of resistance wire with crocodile clips attached to its ends. ● Wrap the wire around the rods of the clamps, as shown in Fig. 1.2. rod of clamp rod of clamp wire insulation crocodile clips stand ohmmeter bench Ω Fig. 1.2 ● Connect the ohmmeter to the crocodile clips, as shown in Fig. 1.2. ● Record the resistance R shown by the ohmmeter. R = ............................................................... ● Five sections of wire are in contact with both rods, as shown in Fig. 1.3. sections of wire in contact with both rods rod rod Fig. 1.3 ● Record the number n of sections of wire that are in contact with both rods. n = ............................................................... [1] (b) Change n by wrapping the wire around the rods a different number of times. Measure R and count n. Continue until you have five sets of values of R and n. 1 Record your results in a table. Include values of (n – n) to three significant figures in your table. [9] 1(c) (i) Plot a graph of R on the y-axis against (n – n) on the x-axis. [3] (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 R and n are related by the equation 1 R = a(n – n) + b where a and b are constants. Use your answers in (c)(iii) to determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] (e) The resistance per unit length r of the wire can be found using a = – xr. Calculate r. Give an appropriate unit. r = ......................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a)(i) Value of raw x to the nearest mm and final value in the range 4.0–8.0 cm. 1 1(a)(ii) Value for R with unit in the range 18.0  ⩽ R ⩽ 30.0 . 1 1(b) Five sets of readings of n and R with correct trend (R decreases as n increases) and without help from the Supervisor scores 4 marks, four sets scores 3 marks etc. 4 Range: nmin ⩽ 3 and nmax ⩾ 9. 1 Column headings: 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. R / . The quantities n and (n – 1 / n) must have no unit. 1 Consistency: All values of raw R must be given to the nearest 0.1 . 1 Significant figures: All (n – 1 / n) values must be given to three significant figures. 1 Calculation: (n – 1 / n) calculated correctly. 1 1(c)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings are no more than 2 cm (one large square) apart. 1 Plotting of points: 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. 1 Quality: All points in the table must be plotted (at least 4) for this mark to be awarded. Trend of points must be negative. It must be possible to draw a straight line that is within ± 0.5  in the R direction of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: Judge by the balance of all points on the grid about the candidate’s line (at least 4 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least 4 points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used must 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. Method of calculation must be correct (not x / y). Gradient sign on answer line matches graph drawn. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at (n – 1 / n) = 0 accurate to half a small square in y direction. 1 1(d) Value of a = candidate’s gradient and value of b = candidate’s intercept. The values must not be written as fractions. 1 Units for a and b correct (e.g.  for a and  for b). 1 1(e) Correct value of r and correct unit (e.g.  m–1) given. 1

More questions on Resistance and resistivity

2 In this experiment, you will investigate an oscillating system. (a) (i) ● You have been provided with two lengths of string and a wooden rod. Tie the strings to the rod at the positions of the lines, as shown in Fig. 2.1. string rod line marked on rod Fig. 2.1 ● Assemble the apparatus as shown in Fig. 2.2. Both split corks should be at a height of 55 cm above the bench. clamp split cork split cork L boss string rod stand 55 cm 38 cm 30 cm Fig. 2.2 ● Adjust the strings in the split corks so that the lower end of the rod is 30 cm above the bench and the upper end of the rod is 38 cm above the bench, as shown in Fig. 2.2. ● Move the stands so that the strings are vertical. ● The horizontal distance between the strings is L, as shown in Fig. 2.2. Measure and record L. L = ......................................................... [1] (ii) ● Push the centre of the rod away from you. Release it and watch its motion. The rod will twist for a while and then swing for a very short time before twisting again and swinging again for a very short time. ● The time from when the rod swings to when it next swings is ts. Measure and record ts. ts = ......................................................... [2] (iii) Estimate the percentage uncertainty in your value of ts. Show your working. percentage uncertainty = ......................................................% [1] (b) (i) ● Leave the strings clamped in the split corks, but slide the string loops off the rod. ● For the longer string, fill the loop with modelling clay to make a pendulum, as shown in Fig. 2.3. modelling clay Fig. 2.3 ● Push the modelling clay a short distance away from you. Take measurements to determine the period T1 of its oscillations. T1 = ......................................................... [1] (ii) Repeat (b)(i) for the shorter string to determine the period T2 of its oscillations. T2 = ......................................................... [1] (iii) Calculate B, where T1T2 B = (T1 – T2). Give an appropriate unit.

Mark scheme: 2(a)(i) Value for L with unit and raw values of L to nearest mm. 1 2(a)(ii) Value for ts with unit and in range 2.0–5.0 s. 1 Evidence of repeat readings for ts. 1 2(a)(iii) Percentage uncertainty in ts based on an absolute uncertainty of 0.2–0.5 s. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(i) Value for T1 with unit. All raw values given to nearest 0.01 s or all raw values given to nearest 0.1 s. 1 2(b)(ii) Value for T2 less than T1. 1 2(b)(iii) Correct calculation of B with unit of s. 1 2(c) Second L < first L. 1 Second value of ts. 1 Second values of T1 and T2. 1 2(d) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 15% leading to a consistent conclusion. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure ts with a reason i.e. difficult to judge when twisting changes to swinging. C Difficult to measure L with a reason: difficult to judge when strings are vertical/hand moves when holding the ruler/difficult to hold ruler still/ruler moves the strings/ruler not horizontal. D Loops move on rod/string slides off rod. E Large uncertainty in B with a reason e.g. difference between T1 and T2 is small. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Record/film/video rod with timer in view. or record/film/video rod and view frame by frame. C Support ruler being used to measure L in a clamp/use set square between clamp and string/use plumb-line/use a spirit level. D Make grooves around rod/add notches to rod/use tape to hold string on rod/use a rough rod. E Tilt rod at steeper angle/increase difference in length of the strings. 1 mark for each point up to a maximum of 4. 4

More questions on Physical quantities