Q106 / 150 · MHT CET 2024 (10 May Shift 1) · Physics
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
- A5 capacitors in parallel and then 2 capacitors series.
- B4 capacitors in parallel and then 3 capacitors series.
- Correct answerC3 capacitors in parallel and then 4 capacitors in series.
- D2 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
Hence, the correct answer is option: 'C'.