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  4. Five capacitors are connected as shown in the figure. Initially, S is opened and all capacitors are uncharged. When S is closed, steady state is obtained. If the potential difference between the points M and N is found to be VM-VN=4 P volt. The value of P is .

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Q. Five capacitors are connected as shown in the figure. Initially, $S$ is opened and all capacitors are uncharged. When $S$ is closed, steady state is obtained. If the potential difference between the points $M$ and $N$ is found to be $V_{M}-V_{N}=4 P$ volt. The value of $P$ is _____.Physics Question Image

Electrostatic Potential and Capacitance

Solution:

Let $q$ be the charge on all the capacitor
image
Apply KVL
$31-\frac{q}{4}-\frac{q}{2}-\frac{q}{4}-7-\frac{q}{6}-\frac{q}{12}=0$
$24=\left[\frac{3+6+3+2+10}{12}\right] q$
$q=12\, \mu C$
Now $V_{N}+\frac{q}{6}+7+\frac{q}{4}=V_{M} $
$V_{M}-V_{N}=12 \,V$