The n identical cells, each of emf x and internal resistance r, connected in series are charged by a dc source of emf y through a resistor R connected in series with it. The current flowing in the circuit is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{y - nx}{R + nr} \)
The n cells in series have a total emf nx and a total internal resistance nr. To charge them, the dc source drives current into their positive terminal, so the emf of the cells opposes the source emf. Applying Kirchhoff’s loop rule around the circuit:
\( y - nx - I(R + nr) = 0 \)
\( \displaystyle I = \frac{y - nx}{R + nr} \)
Charging is possible only when y is greater than nx.