A solenoid of resistance `50Omega` and inductance `80H` is connected to a `200V` battery. How long will it take for the current to reach `50%` of its final equilibrium value? Calculate the maximum energy stored.

Explanation

`i=i_(0)(1-e^(-t//tau))=(E)/(R)(1-e^(-(Rt)/(L)))`
`i=i_(0)//2` , `t`=?
`(i_(0))/(2)=i_(0)(1-e^(-t//tau))`
`e^(-t//tau)=2`
`(t)/(tau)1n e=1n2`
`t=tau1n2=(L1n2)/(R)`
`=(80xx0.693)/(50)=1.1sec`
`U_(max)=(1)/(2)Li_(0)^(2)=(1)/(2)L((E)/(R))^(2)`
`=(1)/(2)xx80xx((200)/(50))^(2)=640J`