An LR circuit having a time constant of 50 ms is connected with an ideal battery of emf `epsilon` . Find the time taken for the magnetic energy stored in the circuti to change from one fourth of the steady state value to half of the steady stae value.

Explanation

`t=(L/R)=50ms=0.05s`
(a) `(i_0)/2=(i_0)(1-e^(-t//0.05))`
`implies (1/2)=1-e^(-t//0.05)`
`implies e^(-t//0.05)=(1/2)`
`implies In e^(-t//0.05)=In(1/4)`
(take In both sides)
`impliest=0.05xx0.693`
`=0.03465s`
`=34.6ms=35ms`
`(b) P=i^(2)R=(E^2)/(R)(1-e^(tR//L))^2`
`Maximum Power =(E^2)/(R)`
so, (E^2)/(2R)=(E^2)/(R)(1-e^(tr/L)^2)`
`implies1-e^(-R//L)=(1)/(sqrt(2))=0.707`
`e^(-R//L)=0.293`
`implies t=50xx1.2275ms`
`=61.2ms` .