1. Data based question. This question is about change of electrical resistance with temperature.

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1 1. Data based question. This question is about change of electrical resistance with temperature. The table below gives values of the resistance R of an electrical component for different values of its temperature T. (Uncertainties in measurement are not shown.) T/ C R/Ω (a) On the grid below, plot a graph to show the variation with temperature T of the resistance R. Show values on the temperature axis from T = 0 C to T = 10 C. (3) (b) (i) Draw a curve that best fits the points you have plotted. Extend your curve to cover the temperature range from 0 C to 10 C. 1

2 (ii) Use your graph to determine the resistance at 0 C and at 10 C. Resistance at 0 C =...Ω Resistance at 10 C =...Ω (2) (c) On your graph, draw a straight-line between the resistance values at 0 C and at 10 C. This line shows the variation with temperature (between 0 C and 10 C) of the resistance, assuming a linear change. (d) (i) Assuming a linear change of resistance with temperature, use your graph to determine the temperature at which the resistance is 3060 Ω. Temperature =... C (ii) Use your answer in (d)(i) to calculate the percentage difference in the temperature for a resistance of 3060 Ω that results from assuming a linear change rather than the non-linear change (3) (Total 11 marks) 2

3 2. This question is about thermal energy transfer through a rod. A student designed an experiment to investigate the variation of temperature along a copper rod when each end is kept at a different temperature. In the experiment, one end of the rod is placed in a container of boiling water at 100 C and the other end is placed in contact with a block of ice at 0.0 C as shown in the diagram. temperature sensors boiling water 100 C copper rod ice 0 C not to scale 3

4 Temperature sensors are placed at 10 cm intervals along the rod. The final steady state temperature θ of each sensor is recorded, together with the corresponding distance x of each sensor from the hot end of the rod. The data points are shown plotted on the axes below. / C x / cm The uncertainty in the measurement of θ is ±2 C. The uncertainty in the measurement of x is negligible. (a) On the graph above, draw the uncertainty in the data points for x = 10 cm, x = 40 cm and x = 70 cm. (2) (b) On the graph above, draw the line of best-fit for the data. 4

5 (c) Explain, by reference to the uncertainties you have indicated, the shape of the line you have drawn (2) (d) (i) Use your graph to estimate the temperature of the rod at x = 55 cm. (ii) Determine the magnitude of the gradient of the line (the temperature gradient) at x = 50 cm. (3) 5

6 (e) The rate of transfer of thermal energy R through the cross-sectional area of the rod is Δθ proportional to the temperture gradient along the rod. At x = 10 cm, R = 43W and Δx Δ θ the magnitude of the temperature gradient is =1.81 C cm 1. At x = 50 cm the value Δx of R is 25 W. Use these data and your answer to d(ii) to suggest whether the rate R of thermal energy transfer is in fact proportional to the temperature gradient (3) (Total 12 marks) 6

7 3. As part of a road-safety campaign, the braking distances of a car were measured. A driver in a particular car was instructed to travel along a straight road at a constant speed v. A signal was given to the driver to stop and he applied the brakes to bring the car to rest in as short a distance as possible. The total distance D travelled by the car after the signal was given was measured for corresponding values of v. A sketch-graph of the results is shown below. v 0 0 (a) State why the sketch graph suggests that D and v are not related by an expression of the form D D =mv + c, where m and c are constants

8 (b) It is suggested that D and v may be related by an expression of the form D = av + bv 2, where a and b are constants. In order to test this suggestion, the data shown below are used. The uncertainties in the measurements of D and v are not shown. v / m s 1 D / m D / v D (i) In the table above, state the unit of. v D (ii) Calculate the magnitude of, to an appropriate number of significant digits, for v v = 22.5 m s 1. 8

9 D v (S.I. units) (c) Data from the table are used to plot a graph of v D (y-axis) against v (x-axis). Some of the data points are shown plotted below v / m s On the graph above, (i) plot the data points for speeds corresponding to 22.5 m s 1 and to 31.5 m s 1. (2) (ii) draw the best-fit line for all the data points. 9

10 (d) Use your graph in (c) to determine (i) the total stopping distance D for a speed of 35 m s 1. (2) (ii) the intercept on the v D axis. (iii) the gradient of the best-fit line. (2) (e) Using your answers to (d)(ii) and (d)(iii), deduce the equation for D in terms of v. D = (f) (i) Use your answer to (e) to calculate the distance D for a speed v of 35.0 m s 1. (ii) Briefly discuss your answers to (d)(i) and (f)(i). (Total 14 marks) 4. This question is about data analysis. 10

11 Data for the refractive index n of a type of glass and wavelength λ of the light transmitted through the glass are shown below. Only the uncertainties in the values of n are significant and these uncertainties are shown by error bars n /nm (a) State why the data do not support the hypothesis that there is a linear relationship between refractive index and wavelength (b) Draw a best-fit line for the data points. (2) 11

12 (c) The rate of change of refractive index D λ with wavelength is referred to as the dispersion. At any particular value of wavelength, D λ is defined by D λ = Δn Δλ Use the graph to determine the value of D λ at a wavelength of 380 nm (4) 12

13 (d) Based on the plotted data, it is suggested that the relationship between n and λ is of the form n = A + B 2 λ where A and B are constants. To test this suggestion, values of n are plotted against values of with the line of best fit is shown below. 1 λ 2. The resulting graph n / 10 m 13

14 (i) Use the graph to determine the value of the constant A (3) (ii) State the significance of the constant A..... (Total 11 marks) 14