Question

Charges Q and 2Q are given to left and right plate of a parallel place capacitor of capacitance $C_o.$ Plates are connected by a resistance R and switch S. At t = 0 switch is closed.

• A. Heat generated across R after long time is $\frac{Q^2}{8C_o}$
• B. Charge on side A of left plate after long time is $\frac{3Q}{4}$
• C. Initial potential difference between plates is $\frac{Q}{2C_o}$
• D. Charge on side D of right plate after long time is $\frac{3Q}{2}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A Heat generated across R after long time is $\frac{Q^2}{8C_o}$
C Initial potential difference between plates is $\frac{Q}{2C_o}$
D Charge on side D of right plate after long time is $\frac{3Q}{2}$

Charges of side A and D remains same.
By Q = CV,
the potential difference at $t=0$ is $V=\frac{Q/2}{C}=\frac{Q}{2C}$
Heat loss = Energy stored in the capacitor =$\frac{q^2}{2C}=\frac{(Q/2{)}^2}{2C_o}=\frac{Q^2}{8C_o}$
After a long time, charge on A will be equal to that of B which is equal to $\frac{3Q}{2}$.