If n identical cells, each of emf E and internal resistance r, are connected in series, write an expression for the terminal p.d.

i. Let n identical cells, each of emf E and internal resistance r, be connected in series. Let the current supplied by this combination to an external resistance R be I.

ii. The equivalent emf of the combination, E_eq = E + E + …….. (n times) = nE

iii. The equivalent internal resistance of the combination,

r_eq = r + r + … (n times)

= nr

iv. The terminal p.d. of the combination is

V = E_eq – Ir_eq = nE – Inr = n (E – Ir)

∴ V = n × terminal p.d. of a single cell

Thus, the terminal p.d. of the series combination is n times that of a single cell.