Q 12-02-067JEE MainJEE Main 2024 (5 Apr, Shift 1)Medium
Three capacitors of capacitances $25\ \mu\text{F}$, $30\ \mu\text{F}$ and $45\ \mu\text{F}$ are connected in parallel to a supply of $100\ \text{V}$. The energy stored in the above combination is $E$. When these capacitors are connected in series to the same supply, the stored energy is $\dfrac{9}{x}E$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 86
Parallel: $C_p = 100\ \mu\text{F}$.
Series: $\dfrac{1}{C_s} = \dfrac{1}{25} + \dfrac{1}{30} + \dfrac{1}{45} = \dfrac{36 + 30 + 20}{900} = \dfrac{86}{900} \Rightarrow C_s = \dfrac{900}{86}\ \mu\text{F}$.
At the same voltage $E \propto C$:
$$\frac{E_s}{E} = \frac{900/86}{100} = \frac{9}{86} \Rightarrow x = 86$$
Solution by Sreeraj P, M.Sc Physics