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Standard XII

Mathematics

Multinomial Theorem

Three capacit...

Question

Three capacitors $C_{1}, C_{2}$ and $C_{3}$ are connected to a battery as shown. With symbols having usual meanings, the correct conditions are :

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

and

V_{1} = V_{2} = V

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

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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 $V = V_{1} + V_{2}$
As $C_{2}$ and $C_{3}$ are in parallel so $V_{2} = V_{3} \Rightarrow Q_{2} / C_{2} = Q_{3} / C_{3}$
As $C_{1}$ and combine $(C_{2}, C_{3})$ are in series, so $V = V_{1} + V_{2}$ or $V = V_{1} + V_{3}$
and also $Q_{1} = Q_{2} + Q_{3}$

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