COMEDK · Physics · 19. Current Electricity

A series combination of 'n' cells of emf 'E' and internal resistance 'r' each, are connected across the external resistance 'R'. If the internal resistance 'r' is negligibly small, then the current 'I' through the external resistance is:

A \(I = \dfrac{E}{R}\)
B \(I = \dfrac{rE}{n}\)
C \(I = \dfrac{nE}{R}\)
D \(I = \dfrac{E}{nR}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(I = \dfrac{nE}{R}\)

Step-by-step Solution

Detailed explanation

The equivalent electromotive force of \(n\) cells connected in series is \(nE\). The equivalent internal resistance of the series combination is \(nr\). The total resistance of the circuit is the sum of the external resistance and the equivalent internal resistance, which is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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