MHT-CET Physics Electrostatics PYQ - Series Condensers

9) Three condensers of capacities \(C_1\), \(C_2\), \(C_3\) are connected in series with a source of emf \(V\). The potentials across the three condensers are in the ratio:

A. \( 1:1:1 \)

B. \( C_1 : C_2 : C_3 \)

C. \( C_1^2 : C_2^2 : C_3^2 \)

D. \( \frac{1}{C_1} : \frac{1}{C_2} : \frac{1}{C_3} \)

Solution:

When capacitors (or condensers) are connected in series, the same charge \(Q\) appears on each capacitor. The potential difference across each capacitor is given by: \[ V_i = \frac{Q}{C_i}. \] Therefore, the ratios of the potentials across the capacitors are: \[ V_1 : V_2 : V_3 = \frac{1}{C_1} : \frac{1}{C_2} : \frac{1}{C_3}. \] Hence, the correct answer is option D.