Three condensers of capacities ' $\mathrm{C}_1$ ', ' $\mathrm{C}_2$ ', ' $\mathrm{C}_3$ ' are connected in…

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
  1. $1: 1: 1$
  2. $\mathrm{C}_1: \mathrm{C}_2: \mathrm{C}_3$
  3. $\mathrm{C}_1^2: \mathrm{C}_2^2: \mathrm{C}_3^2$
  4. $\frac{1}{\mathrm{C}_1}: \frac{1}{\mathrm{C}_2}: \frac{1}{\mathrm{C}_3}$

Solution

When capacitors are connected in series, the charge is same on all the capacitors. $\begin{aligned} & \mathrm{Q}=\mathrm{C}_1 \mathrm{~V}_1=\mathrm{C}_2 \mathrm{~V}_2=\mathrm{C}_3 \mathrm{~V}_3 \\ & \Rightarrow \mathrm{~V}_1: \mathrm{V}_2: \mathrm{V}_3=\frac{1}{\mathrm{C}_1}: \frac{1}{\mathrm{C}_2}: \frac{1}{\mathrm{C}_3} \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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