Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are connected in a configuration to obtain an…

Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are connected in a configuration to obtain an effective capacitance $\frac{6}{13} \mu \mathrm{~F}$. The combination which will achieve this will have
  1. 5 capacitors in parallel and then 2 capacitors series.
  2. 4 capacitors in parallel and then 3 capacitors series.
  3. 3 capacitors in parallel and then 4 capacitors in series.
  4. 2 capacitors in parallel and then 5 capacitors in series.

Solution

As required, equivalent capacitance should be, $\mathrm{C}_{\mathrm{eq}}=\frac{6}{13} \mu \mathrm{~F}$ For combination of three capacitors in parallel and four in series, $\begin{aligned} \therefore & \frac{1}{\mathrm{C}_{\mathrm{eq}}} \end{aligned}=\frac{1}{3 \mathrm{C}}+\left[\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}\right]=\frac{\mathrm{C}+12 \mathrm{C}}{3 \mathrm{C}^2}$ $\therefore \quad$ Required combination is 3 capacitors in parallel and 4 in series

Asked in: MHT CET 2024 (10 May Shift 1)

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