Electrostatics 6 Question 5
5. In the given circuit, with steady current, the potential difference across the capacitor must be
$(2001,2 \mathrm{M})$
(a) $V$
(b) $V / 2$
(c) $V / 3$
(d) $2 V / 3$
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Answer:
Correct Answer: 5. (c)
Solution:
- In steady state condition, no current will flow through the capacitor $C$. Current in the outer circuit,
$$ i=\frac{2 V-V}{2 R+R}=\frac{V}{3 R} $$
Potential difference between $A$ and $B$
$$ \begin{aligned} \quad V_{A}-V+V+i R & =V_{B} \\ \therefore \quad V_{B}-V_{A} & =i R=\frac{V}{3 R} \quad R=\frac{V}{3} \end{aligned} $$
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 $V_{B}>V_{A}$.
