Refer to the figure shown below where the symbols have their usual meanings and select the correct option among the following.

Q_{1} = Q_{2} = Q_{3}

and

V_{1} = V_{2} = V_{3} = V

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Q_{1} = Q_{2} + Q_{3}

and

V = V_{1} + V_{2} + V_{3}

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Q_{1} = Q_{2} + Q_{3}

and

V = V_{1} + V_{2}

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Q_{2} = Q_{3}

V_{2} = V_{3}

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Solution

The correct option is C $Q_{1} = Q_{2} + Q_{3}$ and $V = V_{1} + V_{2}$
Potential difference across $C_{2}$ and $C_{3}$ will be the same as they are in parallel.

So, $V_{2} = V_{3}$

The emf of battery will be

$V = V_{1} + V_{2}$

Now, the charge on the equivalent capacitor of the combination
$C_{2}$ and $C_{3}$ will be equal to charge on $C_{1}$ due to series combination.

Thus, $Q_{1} = Q_{2} + Q_{3}$

Hence, option (c) is the correct answer.

Key concept: Voltage and charge in a mixed combination of capacitors.

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