Three uncharged capacitors of capacities $C_1$, $C_2$ and $C_3$ are connected as shown in the figure. $A, B$…
Three uncharged capacitors of capacities $C_1$, $C_2$ and $C_3$ are connected as shown in the figure. $A, B$ and $C$ are at potentials $V_1, V_2$ and $V_3$, respectively, then the potential at $O$ is
zero
Solution
Total charge in the capacitors (accumulated at point $O$ )
$
Q_{\text {total }}=C_1 V_1+C_2 V_2+C_3 V_3
$
Total capacitance of the combination,
$C_{\text {total }}=C_1+C_2+C_3($ w.r.t. point $O)$
So, potential at $O$,
$
\begin{array}{r}
V=\frac{Q_{\text {total }}}{C_{\text {total }}} \\
=\frac{C_1 V_1+C_2 V_2+C_3 V_3}{C_1+C_2+C_3}
\end{array}
$
