20   11 A student carried out an experiment to calibrate a thermistor. She connected the thermistor in series with a resistor and a power supply as shown. Then she placed the thermistor in a beaker of hot water and used a thermometer to record the temperature θ of the water. V to circuit thermometer water beaker thermistor The student recorded θ and corresponding values of the reading V on the voltmeter as the water cooled. (a) Explain, making reference to charge carriers, why V increased as the water cooled. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over 21   (b) Over a limited temperature range V varies with θ according to the expression V = V0e−bθ where b and V0 are constants. (i) Explain why a graph of ln V against θ would give a straight line. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... 22   (ii) The student’s data is shown in the table below. θ / °C V / V 89.0 1.9 74.0 2.9 53.5 4.9 32.5 9.1 18.5 12.6 3.5 18.7 Plot a graph of ln V against θ on the grid opposite. Use the column provided to show any processed data. (5) (iii) Determine values for b and V0. (4) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... b = ....................................................... V0 = ....................................................... Turn over 23   (Total for Question 11 = 14 marks)