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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 :

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A
Q1=Q2=Q3 and V1=V2=V3+V
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B
Q1=Q2+Q3 and V=V1+V2+V3
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C
Q1=Q2+Q3 and V=V1+V2
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D
Q2=Q3 and V2=V3
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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 $$V={ V }_{ 1 }+{ V }_{ 3 }$$

Physics

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