Question

In the circuit shown in figure, if the charge on capacitor C${}_2$ in steady state is $2x\mu$C , Then x is :

Answer 1

Current in outer loop after steady state $=3A$

Assuming that $20V-ve$ terminal is set as reference of $0V$

Therefore Potential between $3\Omega$ & $5\Omega$ resistors is $11V$

And Potential between $10V$ Source and $5\Omega$ resistor is $-4V$

Consider any 2 loop equations:

$-15+x+\frac{y}{2}=0$

$+10-6+\frac{z}{10}-x=0$

And one charge equation:

$x-y+z=0$

where $x$ is for $C_2$, $y$ is for $C_1$ and $z$ is for $C_3$

After solving the equation, the value of $x$ is 6.

Answer is $x=6$