Question

Two non-ideal batteries are connected in parallel. Consider the following statements:
(A) The equivalent emf is smaller 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

(c) B is correct but A is wrong.

The equivalent emf ${\epsilon }_0$ , when two non-ideal batteries of emfs ${\epsilon }_1$ and ${\epsilon }_2$ and internal resistances r₁ and r₂ respectively are connected in parallel to each other, is given by:

${\epsilon }_0=\frac{{\epsilon }_1{r}_1+{\epsilon }_2{r}_2}{r_1+r_2}$

Thus, the equivalent emf is greater than either of the emfs. Thus, statement A is wrong.

For the parallel combination of the batteries of internal resistance r₁ and r₂, the equivalent internal resistance r is given as

$r=\frac{r_1{r}_2}{r_1+r_2}$

Thus, the value of the resultant resistance is even smaller than either resistance.