A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1. [Figure 2.1] Two resistors P and Q are connected to a power supply of e.m.f. E and negligible internal resistance. The current I is measured. The resistance of resistor P is P. The experiment is repeated for different values of P. It is suggested that I and P are related by the equation E = I(P + Q) where Q is the resistance of resistor Q.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [1] gradient = 1/E
2. [1] y-intercept = Q/E
3. [1] First mark for uncertainties correct. Allow 1 s.f. e.g. 10, 10, 20, 20, 30, 30.
4. [1] Second mark for all second column correct. Allow a mixture of significant figures.
5. [1] Six points plotted correctly. Must be accurate to less than half a small square. No "blobs”. Diameter of points must be less than half a small square.
6. [1] Error bars in P plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical.
7. [1] Line of best fit drawn. If points are plotted correctly then lower end of line should pass between (200, 32) and (200, 34) and upper end of line should pass between (600, 88) and (600, 91).
8. [1] Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted.
9. [1] Gradient determined with a triangle that is at least half the length of the drawn line.
10. [1] uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
11. [1] y-intercept determined by substitution of correct point into y = mx + c.
12. [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)
13. [1] E determined using gradient and units for E and Q with correct power of ten. E = 1 / gradient 2(c)(iii)
14. [1] Q determined using y-intercept and E and Q given to 2 or 3 significant figures. Correct substitution of numbers must be seen. Q = E x y-intercept = E ×2(c)(iv) = y-intercept 2(c)(iv) / gradient 2(c)(iii)
15. [1] % uncertainty in E = % uncertainty in gradient
16. [1] % uncertainty in Q = % uncertainty in E + % uncertainty in y-intercept or % uncertainty in Q = % uncertainty in gradient + % uncertainty in y-intercept. Correct substitution of numbers must be seen.
17. Maximum/minimum methods: Max Q = max y-intercept × max E or min y-intercept / min gradient
18. Min Q = min y-intercept × min E or min y-intercept / max gradient