Seven capacitors, each of capacitance $2 \mu \mathrm{F},$ are to be connected in a configuration to obtain…
Seven capacitors, each of capacitance $2 \mu \mathrm{F},$ are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right) \mu \mathrm{F} .$ Which of the combinations, shown in figures below, will achieve the desired value?
Solution
As required equivalent capacitance should be
$C_{\mathrm{eq}}=\frac{6}{13} \mu \mathrm{F}$
Therefore three capacitors must be in parallel and 4 must
be in series with it.
$\frac{1}{\mathrm{C}_{\mathrm{eq}}}=\left[\frac{1}{3 \mathrm{C}}\right]+\left[\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}\right]$
$C_{\mathrm{eq}}=\frac{3 \mathrm{C}}{13}=\frac{6}{13} \mu \mathrm{F} \quad[$ as $\mathrm{C}=2 \mu \mathrm{F}]$
So, desired combination will be as below:
