Q 12-03-220JEE MainJEE Main 2020 (8 Jan, Shift 2)Medium
The series combination of two batteries, both of the same emf $10$ V, but different internal resistance of $20\ \Omega$ and $5\ \Omega$, is connected to the parallel combination of two resistors $30\ \Omega$ and $x\ \Omega$. The voltage difference across the battery of internal resistance $20\ \Omega$ is zero, the value of $x$ (in $\Omega$) is ______.
Numerical value type. Enter your answer.
Answer: 30
Terminal voltage of the $20\ \Omega$ battery: $10 - 20I = 0$, so $I = 0.5$ A.
The total emf is $20$ V and the total internal resistance $25\ \Omega$:
$$I = \frac{20}{25 + R_{\text{ext}}} = 0.5 \Rightarrow R_{\text{ext}} = 15\ \Omega$$
$$\frac{30x}{30 + x} = 15 \Rightarrow x = 30\ \Omega$$
Solution by Sreeraj P, M.Sc Physics