A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1. [Figure 2.1] Resistors, each of resistance R, are connected in parallel between P and Q. The current I is measured. The experiment is repeated for different numbers n of resistors between P and Q. It is suggested that I and n are related by the equation E = I (R/n + r) where E is the electromotive force (e.m.f.) and r is the internal resistance of the power supply.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [1] gradient = R/E
2. [1] y-intercept = r/E
3. [1] Correct calculation of 1/I for all rows in Fig. 2.2.
4. [1] absolute uncertainties in 1/I from ±2 (or ±1) to ±0.2, ±0.3 or ±0.4. Allow a mixture of significant figures.
5. [1] Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square.
6. [1] Error bars in 1/I 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. Points must be balanced. Line should pass to the left of (0.50, 29.6) and line should pass between (0.210, 16) and (0.225, 16).
8. [1] Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted.
9. [1] Gradient determined with clear substitution of points from line of best fit into Δy/Δx. Distance between points must be 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 into y = mx + c.
12. [1] y-intercept of worst acceptable line determined by substitution into y = mx + c. 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) Do not allow if false origin used.
13. [1] E calculated using gradient. Correct substitution of numbers required. E = R/gradient = 470/gradient(c)(iii)
14. [1] r calculated using y-intercept. Correct substitution of numbers required. r = E × y-intercept
15. [1] E and r determined using correct method with: Unit of E with correct power of ten – e.g. V, AΩ Unit of r with correct power of ten – e.g. Ω, VA⁻¹ E and r given to 2 or 3 significant figures.
16. [1] Percentage uncertainty in r determined. Correct substitution of numbers required. %uncertainty in gradient + %uncertainty in R (1.06%) + %uncertainty in y-intercept or %uncertainty in E + %uncertainty in y-intercept Maximum/minimum methods: max r = max y-intercept × max E max r = max y-intercept × (max R (475))/min gradient min r = min y-intercept × min E min r = min y-intercept × (min R (465))/max gradient