Q 12-02-097JEE MainJEE Main 2023 (11 Apr, Shift 2)Hard
In the given circuit, $C_1=2\ \mu\text{F}$, $C_2=0.2\ \mu\text{F}$, $C_3=2\ \mu\text{F}$, $C_4=4\ \mu\text{F}$, $C_5=2\ \mu\text{F}$, $C_6=2\ \mu\text{F}$. The charge stored on capacitor $C_4$ is ______ $\mu\text{C}$.
Numerical value type. Enter your answer.
Answer: 4
$C_3$, $C_4$, $C_5$ are in series: $\dfrac1{C'}=\dfrac12+\dfrac14+\dfrac12\Rightarrow C'=0.8\ \mu\text{F}$.
In parallel with $C_2$: $1.0\ \mu\text{F}$. In series with $C_1$ and $C_6$: $\dfrac1{C}=\dfrac12+1+\dfrac12\Rightarrow C=0.5\ \mu\text{F}$.
Total charge $=5\ \mu\text{C}$, so the voltage across the middle combination is $\dfrac{5}{1.0}=5\ \text{V}$.
Charge on the $C_3C_4C_5$ chain (and on $C_4$) $=0.8\times5=4\ \mu\text{C}$.
Solution by Sreeraj P, M.Sc Physics