A parallel combination of three condensers of capacities ' $2 \mathrm{C}$, ' $\mathrm{C}$ ' and '…
A parallel combination of three condensers of capacities ' $2 \mathrm{C}$, ' $\mathrm{C}$ ' and ' $\mathrm{C} / 2$ ' is connected
Across $10 \mathrm{~V}$ battery. All the condensers are fully charged to charges ' $\mathrm{Q}_1$ ', ' $\mathrm{Q}_2$ ' and ' $\mathrm{Q}$ 3' respectively. The ratio $\mathrm{Q}_1: \mathrm{Q}_2: \mathrm{Q}_3$ is
$4: 1: 2$
$1: 4: 2$
$1: 2: 4$
$4: 2: 1$
Solution
In parallel combination the potential drop across each capacitor is same.
$\begin{aligned} & \therefore \Delta V=\frac{Q_1}{C_1}=\frac{Q_2}{C_2}=\frac{Q_3}{C_3} \\ & \Rightarrow \Delta V=\frac{Q_1}{2 C}=\frac{Q_2}{C}=\frac{Q_3}{(C / 2)} \\ & \Rightarrow(C \Delta V)=\frac{Q_1}{2}=\frac{Q_2}{1}=\frac{Q_3}{1 / 2} \\ & \therefore Q_1=2 \times(C \Delta V), Q_2=1 \times(C \Delta V) \text { and } Q_3=\frac{1}{2} \times(C \Delta V) \\ & \therefore Q_1: Q_2: Q_3=2: 1: 0.5 \\ & \Rightarrow Q_1: Q_2: Q_2=4: 2: 1\end{aligned}$
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