Question 534: Electrostats & Capacitance

Question

Which of the following combination of 7 identical capacitors each of $$2 \mu \mathrm{F}$$ gives a capacitance of $$\frac{10}{11} \mu \mathrm{F}$$ ?

Accepted Answer

For $$\mathrm{n}$$ identical capacitors connected in series, the equivalent capacitance is, $$\mathrm{C}_{\mathrm{s}}=\frac{\mathrm{C}}{\mathrm{n}}$$
Similarly, for $$\mathrm{m}$$ identical capacitors connected parallel to each other, the equivalent capacitance is, $$\mathrm{C}_{\mathrm{p}}=\mathrm{mC}$$
Assuming the two combinations are connected in series, the net capacitance,
$$\begin{aligned}
& \frac{1}{\mathrm{C}_{	ext {net }}}=\frac{1}{\mathrm{mC}}+\frac{\mathrm{n}}{\mathrm{C}}=\frac{11}{10} \mu \mathrm{F} \quad \ldots .\left(\because \mathrm{C}_{	ext {net }}=\frac{10}{11} \mu \mathrm{F}ight) \
& 	herefore 	ext { for } C=2 \mu \mathrm{F} 	ext {, } \
& \frac{11 	imes 2}{10}=\frac{1}{m}+n \
& 	herefore \quad \frac{1}{m}+n=\frac{11}{5} \quad 	ext{..... (i)}\
\end{aligned}$$
Substituting the values for $$m$$ and $$n$$ in equation (i) from each option, the correct answer can be found to be (A).

Answer

5 in parallel and 2 in series

Answer

4 in parallel and 3 in series

Answer

3 in parallel and 4 in series

Answer

2 in parallel and 5 in series

Electrostats & Capacitance

Which of the following combination of 7 identical capacitors each of $2 \mu \mathrm{F} gives a capacitance of \frac{10}{11} \mu \mathrm{F}$ ?

Choose the correct answer: