Electrostatics 5 Question 8
9. In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5 \mu F$. All values in the circuit are in $\mu F$.
(Main 2019, 12 Jan II)
(a) $\frac{6}{5} \mu F$
(b) $4 \mu F$
(c) $\frac{7}{10} \mu F$
(d) $\frac{7}{11} \mu F$
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Solution:
Key Idea Two capacitors $C _1$ and $C _2$, if connected in series, then their equivalent capacitance is
If they are connected in parallel, then their equivalent capacitance is, $C _{eq}=C _1+C _2$.
We simplify given circuit as
$$ \begin{array}{ll} \text { So, } & C _{A B}=\frac{C \times 7 / 3}{C+7 / 3}=\frac{1}{2} \\ \Rightarrow & \frac{7 C}{3}=\frac{C}{2}+\frac{7}{6} \\ \Rightarrow & \frac{14-3}{6} C=\frac{7}{6} \Rightarrow C=\frac{7}{11} \mu F \end{array} $$
