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(D) In a parallel combination,the potential difference across each capacitor is the same.Let the potential difference be $\Delta V = 10 \ V$.The charg

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$4: 2: 1$

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(D) In a parallel combination,the potential difference across each capacitor is the same.Let the potential difference be $\Delta V = 10 \ V$.The charge on a capacitor is given by $Q = C \Delta V$.For the three capacitors:$Q_1 = C_1 \Delta V = (2C) \Delta V = 2C \Delta V$$Q_2 = C_2 \Delta V = (C) \Delta V = C \Delta V$$Q_3 = C_3 \Delta V = (C/2) \Delta V = 0.5C \Delta V$Now,the ratio $Q_1: Q_2: Q_3$ is:$Q_1: Q_2: Q_3 = 2C \Delta V : C \Delta V : 0.5C \Delta V$Dividing by $C \Delta V$,we get:$Q_1: Q_2: Q_3 = 2 : 1 : 0.5$Multiplying by $2$ to express in integers:$Q_1: Q_2: Q_3 = 4 : 2 : 1$.

$A$ parallel combination of three capacitors of capacities $2C$,$C$,and $C/2$ is connected across a $10 \ V$ battery. All the capacitors are fully charged to charges $Q_1$,$Q_2$,and $Q_3$ respectively. The ratio $Q_1: Q_2: Q_3$ is

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