MHT CET · Physics · Capacitance

Three condensers of capacities \(\mathrm{C}_{1}, \mathrm{C}_{2}, \mathrm{C}_{3}\) are connected in series with a source of e.m.f. \(V\). The potentials across the three condensers are in the ratio of

A \(\mathrm{C}_{1}: \mathrm{C}_{2}: \mathrm{C}_{3}\)
B \(C_{1}^{2}: C_{2}^{2}: C_{3}^{2}\)
C \(1: 1: 1\)
D \(\frac{1}{\mathrm{C}_{1}}: \frac{1}{\mathrm{C}_{2}}: \frac{1}{\mathrm{C}_{3}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{\mathrm{C}_{1}}: \frac{1}{\mathrm{C}_{2}}: \frac{1}{\mathrm{C}_{3}}\)

Step-by-step Solution

Detailed explanation

When capacitors are connected in series, the charge is the same on all the capacitors.
\(
\begin{array}{l}
\mathrm{Q}=\mathrm{C}_{1} \mathrm{~V}_{1}=\mathrm{C}_{2} \mathrm{~V}_{2}=\mathrm{C}_{7} \mathrm{~V}_{3} \\
\text { Or } \frac{V_{1}}{\frac{1}{C_{1}}}=\frac{V_{2}}{\frac{1}{C_{2}}}=\frac{V_{3}}{\frac{1}{C_{3}}}
\end{array}
\)

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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