A student investigates the current in a coil and a resistor connected in series, as shown in Fig. 1.1. [Figure 1.1] The student connects a high-voltage d.c. power supply and a switch across the series combination. When the switch is closed, it takes time t for the current in the resistor of resistance R to reach a maximum value. The time t is a few milliseconds. There are a number of different unmarked resistors available. It is suggested that the relationship between t and R is t = KN²A / LR where N is the number of turns of wire on the coil, A is the cross-sectional area of the coil, L is the length of the coil and K is a constant. Design a laboratory experiment to test the relationship between t and R. Explain how your results could be used to determine a value for K. 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.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] R is the independent variable and t is the dependent variable or vary R and measure t
2. [1] keep the number of turns on the coil/N constant
3. [1] labelled diagram or correct symbols including: labelled (d.c.) power supply; switch in series with power supply, resistor and coil; complete workable circuit
4. [1] circuit diagram to measure R, e.g. ammeter and voltmeter correctly positioned or R connected to ohmmeter with no other connections (not ohmmeter in main circuit)
5. [1] method to determine t (of a few milliseconds) e.g. use (storage) oscilloscope or current/voltage sensor connected to datalogger/computer
6. [1] method to determine A, e.g. micrometer/calipers to determine diameter of coil and A = πd²/4
7. [1] plot a graph of t against 1 / R (allow log t against log R)
8. [1] relationship valid if a straight line passing through the origin is produced (allow gradient = −1 for graph of log t against log R)
9. [1] K = gradient × L / AN²
10. D1 open switch/switch off (high voltage) circuit before changing the resistor/touching components or ensure no bare wires/use shrouded connectors
11. D2 wear (insulating) gloves to prevent electric shock/electrocution
12. D3 keep A and L constant
13. D4 use ruler/calipers to measure L
14. D5 repeat measurements of diameter in different directions/at points along the coil and average
15. D6 method to determine R e.g. R = V/I linked to correct circuit diagram for ammeter/voltmeter method or measure resistance using ohmmeter
16. D7 repeat experiment for each value of R and average t
17. D8 method to determine t: use of time-base from oscilloscope explained or use of time axis of output from data logger/computer explained
18. D9 use smaller values of R to increase I
19. D10 reduce L or increase N or increase A to increase t