Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in…
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.
- Both Statement-I and Statement-II are false
- Statement-I is false but Statement-II is true
- Both Statement-I and Statement-II are true
- Statement-I is true but Statement-II is false
Solution
$\begin{aligned}
& \frac{1}{r_{\mathrm{eq}}}=\frac{1}{r_1}+\frac{1}{r_2} \\ & \frac{E_{\mathrm{eq}}}{r_{\mathrm{eq}}}=\frac{E_1}{r_1}+\frac{E_2}{r_2}
\end{aligned}$
If $E_1=E_2$ and $r_1=r_2, E_{\text {eq }}=E_1=E_2$
$\therefore$ Statement 1 is false.
$r_{\text {eq }}$ is less then both $r_1$ and $r_2$
$\therefore$ Statement II is true
Asked in: JEE Main 2025 (22 Jan Shift 1)