Question

For the circuit shown, which of the following statements is true ?

• A. $With \, S_1 \, closed, \, V_1=15V,V_2=20V $
• B. $With \, S_3 \, closed, \, V_1=V_2=25V $
• 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 $

Answer 1

Answer: (D)

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,
$\, \, \, \, \, \, \, \, \, V_1=30 \, V \, and \, V_2=20 V. $