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  4. In the given circuit, with steady current, the potential difference across the capacitor must be

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Q. In the given circuit, with steady current, the potential difference across the capacitor must bePhysics Question Image

IIT JEEIIT JEE 2001Electrostatic Potential and Capacitance

Solution:

In steady state condition, no
current will flow through the
capacitor $C$. Current in the outer circuit,
$i= \frac {2V-V}{2R+R}= \frac {V}{3R} $
Potential difference between $A$ and $B$
$V_A-V+V+iR=V_B $
$\therefore V_B-V_A=iR= \left(\frac {V}{3R}\right)R= \frac {V}{3} $
NOTE In this problem charge stored in the capacitor can also be
asked, which is equal to $q=C \frac {V}{3} $ with positive charge on $B$ side and
negative on $A$ side because $V_B >V_A. $

Solution Image