Question

Two non-ideal batteries are connected in series. Consider the following statements:
(A) The equivalent emf is larger than either of the two emfs.
(B) The equivalent internal resistance is smaller than either of the two internal resistances.

(a) A and B are correct.
(b) A is correct but B is wrong.
(c) B is correct but A is wrong.
(d) A and B are wrong.

Answer 1

(b) A is correct but B is wrong.

Let the emfs of the batteries be e₁ and e₂, and their respective resistances be r₁ and r₂.

Since the batteries are connected in series, the equivalent emf will be the sum of the emf of the two batteries ( e = e₁ + e₂) .
Thus, e > e₁ and e > e₂
Thus, the equivalent emf is larger than either of the two emfs. Hence, statement A is correct.

Since the batteries are connected in series, the equivalent internal resistance (r) of the combination will be the sum of the internal resistance of the two batteries ( r = r₁ + r₂).
r > r₁ and r > r₂

Thus, the equivalent internal resistance is greater that either of the two resistances. Hence, statement B is wrong.