MHT CET · Physics · Capacitance

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

A 5 capacitors in parallel and then 2 capacitors series.
B 4 capacitors in parallel and then 3 capacitors series.
C 3 capacitors in parallel and then 4 capacitors in series.
D 2 capacitors in parallel and then 5 capacitors in series.

Verified Solution

Answer & Solution

Correct Answer

(C) 3 capacitors in parallel and then 4 capacitors in series.

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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