Question

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

• A. \(C_1 : C_2 : C_3\)
• B. \(C_1^2 : C_2^2 : C_3^2\)
• C. \(1 : 1 : 1\)
• D. \(\dfrac{1}{C_1} : \dfrac{1}{C_2} : \dfrac{1}{C_3}\)

Hint:

In series combination of capacitors, voltage divides inversely with capacitance.

Answer 1

The Correct Option is D

Step 1: Property of capacitors in series.
When capacitors are connected in series, the charge on each capacitor is the same.

Step 2: Relation between potential and capacitance.
\[ V = \frac{Q}{C} \]

Step 3: Ratio of potentials.
\[ V_1 : V_2 : V_3 = \frac{Q}{C_1} : \frac{Q}{C_2} : \frac{Q}{C_3} \] \[ = \frac{1}{C_1} : \frac{1}{C_2} : \frac{1}{C_3} \]