Question

Two non-ideal batteries are connected in parallel. Then
(A) the equivalent emf is less than either of the two emfs.
(B) the equivalent internal resistance is less than either of the two internal resistances.

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

Answer 1

The correct option is C only B is 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 $E$,

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

$E_{eq}=E\left(\frac{r_2+r_1}{r_1+r_2}\right)=E$
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 is correct.