JEE Main 2025 — Current Electricity Question with Solution

When two non-ideal batteries are connected in parallel, their equivalent emf is

$$E_{eq}=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}}{\frac{1}{r_1}+\frac{1}{r_2}}\Rightarrow E_{eq}=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}$$

If emf of both cells is same say E,

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

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 1 is correct.