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Parallel and Series Combination of Capacitors

In figure, th...

Question

In figure, three capacitors $C_{1}, C_{2}$ and $C_{3}$ are joined to a battery. With symbols having their usual meaning, the correct conditions will be

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}

and

V_{2} = V_{3}

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Solution

The correct option is C $Q_{1} = Q_{2} + Q_{3}$ and $V = V_{1} + V_{2}$
The given circuit is a combination of capacitors in series and in parellel.

We know that in series combination charge remains same and in parallel combination of capacitors voltage remains same.
$⟹ Q_{1} = Q_{2} + Q_{3}$
also, $V_{2} = V_{3}$
$∴$ Total voltage V will be equal to the combination of voltage across $C_{1}$ and voltage across parallel combinaton of $C_{2}$ and $C_{3}$ .
So, $V = V_{1} + V_{2}$ and $Q_{1} = Q_{2} + Q_{3}$

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