Question

A charged capacitor is discharged through a resistance. The time constant of the circuit is $\eta$. Then the value of time constant for the power dissipated through the resistance will be

• A. $\eta$
• B. $2\eta$
• C. $\eta /2$
• D. zero

Answer 1

The correct option is C $\eta /2$

During discharge the current though resistance is $i=i_0{e}^{-t/\eta }$ where $\eta =$ time constant.
Power dissipation through resistor R is $P=i^{2}R=i_0^2{e}^{-2t/\eta }R=P_0{e}^{-t/\left(\eta /2\right)}$
Thus time constant becomes $\frac{\eta }{2}$