Electrostatics 5 Question 29
31. For the circuit shown, which of the following statements is true?
(1999, 2M)
(a) With $S _1$ closed, $V _1=15 V, V _2=20 V$
(b) With $S _3$ closed, $V _1=V _2=25 V$
(c) With $S _1$ and $S _2$ closed, $V _1=V _2=0$
(d) With $S _3$ closed, $V _1=30 V, V _2=20 V$
Show Answer
Solution:
- When $S _3$ is closed, due to attraction with opposite charge, no flow of charge takes place through $S _3$. Therefore, potential difference across capacitor plates remains unchanged or $V _1=30 V$ and $V _2=20 V$.
Alternate Solution
Charges on the capacitors are
$$ q _1=(30)(2)=60 pC $$
and $q _2=(20)(3)=60 pC$ or $q _1=q _2=q$ (say)
The situation is similar as the two capacitors in series are first charged with a battery of emf $50 V$ and then disconnected.
$\therefore$ When $S _3$ is closed,
$$ \text { and } \quad V _2=20 V \text {. } $$
