A student investigates the current in a circuit containing a cell, as shown in Fig. 2.1. A E r R1 R2 P Q Fig. 2.1 The student connects two resistors of resistances R₁ and R₂ between P and Q. The ammeter measures the current I. The student repeats the experiment with different resistors between P and Q. It is suggested that I, R₁ and R₂ are related by the equation E = I(R₁ + R₂ + r) where E is the electromotive force (e.m.f.) and r is the internal resistance of the cell.

Mark scheme

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

1. 2(a) gradient = 1/E
2. 2(a) y-intercept = r/E
3. 2(b) Values of (R1 + R2) and 1/I as shown above.
4. 2(b) Absolute uncertainties in (R1 + R2) from ± (2.75 or 2.8 or 3) to ± (5.15 or 5.2 or 5).
5. 2(c)(i) Six points plotted correctly. Must be accurate to the nearest half a small square. Diameter of points must be less than half a small square.
6. 2(c)(i) Error bars in (R1 + R2) plotted correctly. All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
7. 2(c)(ii) Line of best fit drawn covers all points. Points must be balanced. Do not allow line from top point to bottom point. Line must pass between (61.0, 65.0) and (63.5, 65.0) and between (96.5, 95.0) and (98.5, 95.0).
8. 2(c)(ii) Worst acceptable line drawn (steepest or shallowest possible line that passes through all error bars). All error bars must be plotted.
9. 2(c)(iii) Gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least half the length of the drawn line.
10. 2(c)(iii) Gradient of worst acceptable line determined.
11. 2(c)(iii) uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
12. 2(c)(iv) y-intercept determined by substitution of correct point into y = mx + c.
13. 2(c)(iv) y-intercept of worst acceptable line determined by substitution into y = mx + c.
14. 2(c)(iv) 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 ECF from false origin method.
15. 2(d)(i) E determined using gradient and E and r given to two or three significant figures. E = 1/gradient
16. 2(d)(i) r determined using y-intercept with correct substitution and units with correct power of ten for E and r. r = y-intercept/gradient or r = E × y-intercept
17. 2(d)(ii) Absolute uncertainty in E determined with method shown e.g. ΔE = Δgradient / gradient × E or correct substitution for max/min methods e.g. ΔE = E / min gradient – E / max gradient
18. 2(e) Value of R2 determined from (d)(i) or (c)(iii) and (c)(iv), with correct substitution and correct power of ten. R2 = E / 0.0075 – (22 + r) or R2 = 1 / (0.0075 × gradient) – (22 + r)