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Obtain the equivalent capacitance of the network in Fig. For a $300 \mathrm{~V}$ supply, determine the charge and voltage across each capacitor.


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Verified Answer

Capacitance between $\mathrm{C}$ and $\mathrm{F}\left(\mathrm{C}_2, \mathrm{C}_3\right.$ in series $)=200$ / $2=100 \mathrm{pF}$
Capacitance between $B$ and $G$ (in parallel) $=100+100=200 \mathrm{pF}$
Capacitance between $\mathrm{A}$ and $\mathrm{G}$ (in series)
$$
=(100 \times 200) /(100+200)=(200 / 3) \mathrm{pF}
$$
Potential difference of $300 \mathrm{~V}$ between $\mathrm{A}$ and $\mathrm{G}$ divided between points $A$ and $B$ and points $B$ and $G$, in the inverse ratio of the capacitance between them. Thus, Potential difference between $\mathrm{A}$ and $\mathrm{B}=200 \mathrm{~V}$
Potential difference between $\mathrm{B}$ and $\mathrm{G}=100 \mathrm{~V}$
Hence, $\mathrm{V}_4=200 \mathrm{~V}$ and $\mathrm{q}_4=\mathrm{C}_4 \mathrm{~V}_4$
$$
\begin{aligned}
\quad=2 \times 10^{-8} \mathrm{C} \\
\mathrm{V}_1 &=100 \mathrm{~V} \text { and } \mathrm{q}_1=\mathrm{C}_1 \mathrm{~V}_1=10^{-8} \mathrm{C} \\
\mathrm{V}_2 &=\mathrm{V}_3=50 \mathrm{~V} \text { and } \mathrm{q}_2=\mathrm{q}_3=\mathrm{C}_2 \mathrm{~V}_2=\mathrm{C}_3 \mathrm{~V}_3 \\
&=10^{-8} \mathrm{C}
\end{aligned}
$$
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