Shown in the figure is a circular loop of radius, r and resistance R. A variable magnetic field of induction `B=e^(-t)` is established inside the coil. If the key (K) is closed at t=0 , the electrical power developed at the instant is equal to

Explanation

`E= (-d phi)/(dt)= -A. (dB)/(dt)`
`E= - pi r^(2) (d)/(dt) (e^(-t)), E= pi r^(2) e^(-t)`
`P= (E^(2))/(R )= (pi^(2) r^(2) e^(-2t))/(R )`
Note: At `t=0, P= (pi^(2)r^(4))/(R )`