Question

If n identical cells, each of emf E and internal resistance r, are connected in parallel, derive an expression for the current supplied by this combination to external resistance R. Prove that the combination supplies current almost n times the current supplied by a single cell, when the external resistance R is much smaller than the internal resistance of the parallel combination of the cells.

Answer 1

i. Consider n identical cells, each of emf E and internal resistance r, connected in parallel.

ii. Let the current supplied by the combination to the external resistance R be I.

In this case, the equivalent emf of the combination is E.

iii. The equivalent internal resistance r’ of the combination is,

iv. But V = IR is the terminal p.d. across each cell.

v. Hence, the current supplied by each cell,

I = \(\frac{E-V}{r}\)

vi. This gives the current supplied by the combination to the external resistance as

Thus, current I = n × current supplied by a single cell

This proves that, the current supplied by the combination is n times the current supplied by a single cell.