Given below are two statements:
**Statement-I:** The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
**Statement-II:** The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.
Answer: (B) Statement-I is false but Statement-II is true
For two cells $(\varepsilon_1, r_1)$ and $(\varepsilon_2, r_2)$ in parallel:
$$\varepsilon_{eq} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2}, \qquad r_{eq} = \frac{r_1 r_2}{r_1 + r_2}$$
$\varepsilon_{eq}$ is a weighted average of $\varepsilon_1$ and $\varepsilon_2$, so it lies **between** the two emfs; it is not smaller than both. Statement-I is false.
$r_{eq}$ is the parallel combination of $r_1$ and $r_2$, which is always smaller than each of them. Statement-II is true.
Solution by Sreeraj P, M.Sc Physics