Question

A Circuit contains two identical resistors of resistance $R$ and a capacitor of capacitance $C1$ connected to a battery that provides an emf of $V$, as shown above.
At time zero the Capacitor is initially uncharged. Which of the following expressions would represent the power dissipated in resistor $R_2$ after a long time?

• A. 0
• B. $\frac{1}{{}_{e}RC}$
• C. $\frac{V^2}{R}$
• D. $\frac{V^2}{2R}$
• E. $\frac{V^2}{4R}$

Answer 1

The correct option is A 0

After a long time steady state is reached , now the voltage across capacitor is constant (equal to the voltage of battery) hence current (which is a time derivative of voltage ) becomes zero . Therefore power dissipated in resistor would become zero as $P=I^{2}R$ or $P=0^2\times R=0$