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

• A. $Q_{1}=Q_{2}=Q_{3}$ and $V_{1}=V_{2}=V_{3}+V$
• B. $Q_{1}=Q_{2}+Q_{3}$ and $V=V_{1}+V_{2}+V_{3}$
• C. $Q_{1}=Q_{2}+Q_{3}$ and $V=V_{1}+V_{2}$
• D. $Q_{2}=Q_{3}$ and $V_{2}=V_{3}$

Answer 1

Answer: (C)

At junction $A, Q_{1}$ 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 $\left.V_{3}\right) .$.
Hence, $V=V_{1}+V_{2}$ or $V=V_{1}+V_{3}$