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In the figure...

Question

In the 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 :

A

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

and

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

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B

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

and

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

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C

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

and

V = V_{1} + V_{2}

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D

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 $V = V_{1} + V_{2}$
At junction point $A$ , $Q_{1}$ will be divided into $Q_{2}$ and $Q_{3}$ .
Hence, $Q_{1} = Q_{2} + Q_{3}$ .
$C_{2}$ and $C_{3}$ are in parallel, so potential on them will be the same,
i.e $V_{2} = V_{3}$
$V$ will be divided into $V_{1}$ and $V_{2}$ (or $V_{3}$ )
Hence, $V = V_{1} + V_{2}$ or $V = V_{1} + V_{3}$

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