Electrostatics 5 Question 8
9. In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5 \mu \mathrm{F}$. All values in the circuit are in $\mu \mathrm{F}$.
(Main 2019, 12 Jan II)
(a) $\frac{6}{5} \mu \mathrm{F}$
(b) $4 \mu \mathrm{F}$
(c) $\frac{7}{10} \mu \mathrm{F}$
(d) $\frac{7}{11} \mu \mathrm{F}$
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Answer:
Correct Answer: 9. (d)
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, $C_{\mathrm{eq}}=C_{1}+C_{2}$.
We simplify given circuit as
$ \begin{array}{ll} \text { So, } & C_{A B}=\frac{C \times 7 / 3}{C+7 / 3}=\frac{1}{2} \quad(given)\\ \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 \mathrm{F} \end{array} $
