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. both A and B are correct
• B. A is correct but B is wrong
• C. B is correct but A is wrong
• D. both A ad B are wrong

Answer 1

The correct option is A both A and B are correct

When two non-ideal batteries are connected in parallel, their equivalent emf is
$E_{eq}=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}}{\frac{1}{r_1}+\frac{1}{r_2}}$

$E_{eq}=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}$

If emf of both cells is same say $E$,
$E_{eq}=\frac{E{r}_2+E{r}_1}{r_1+r_2}$
$E_{eq}=E\frac{r_2+r_1}{r_1+r_2}=E$

Hence, equivalent emf is equal to emf of the single cell.
Also, when two non-ideal batteries are connected in parallel, their equivalent resistance is
$r_{eq}=\frac{r_1{r}_2}{r_1+r_2}$

Hence, the equivalent internal resistance is smaller than either of the two internal resistances.
Therefore, B as well as A is correct.