The correct answer is B because:

Write down the relevant equation for e.m.f:
- $Ɛ_{T} = I (r_{T} + R_{E})$
Find the total external resistance of the circuit RE from the two resistors in parallel
- $\frac{1}{R_{E}} = (\frac{1}{R_{1}} + \frac{1}{R_{2}})$
- $R_{E} = {(\frac{1}{R} + \frac{1}{R})}^{- 1}$
- $R_{E} = {(\frac{2}{R})}^{- 1} = \frac{R}{2}$
Find $r_{T}$ from the two cells in series:
- Series: $r_{T} = R_{1} + R_{2} = r + r = 2 r$
Find ƐT from the two cells in series:
- Series: $Ɛ_{T} = Ɛ + Ɛ = 2 Ɛ$
Substitute the results for ƐT, RT and rT into the formula for ƐT to obtain
- $2 Ɛ = I (2 r + \frac{R}{2})$
Rearrange for I:
- $I = \frac{2 Ɛ}{(2 r + \frac{R}{2})}$

A is incorrect due to the misconception that the total e.m.f in the circuit equals the e.m.f of a single cell.

C is incorrect because specific values for e.m.f. and internal resistance have not been calculated and substituted into the equation.

D is incorrect because internal resistance has not been substituted into the equation.

This algebraic question involves manipulating equations from various topics. Common pitfalls include summing e.m.f.’s in series and adding internal resistances for the cells. While substituting expressions into the total e.m.f. formula be vigilant about factors of 2 and ensure numerical accuracy after manipulation.

EMF & Internal Resistance (OCR AS Physics)

Exam Questions