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

Explanation

Here, `R = 50 Omega, L = 80 H`,
`E = 200 V, t = ?`
`I = (50)/(100) I_(0)`
`tau = (L)/( R) = (80)/(50) = (8)/(5)s , I_(0) = (E)/(R ) = (200)/(50) = 4 A`
From `I = I_(0) (1 - e^(-t//tau))`,
`t = tau log_(e) 2 = (8)/(5) xx 0.693 = 1.109 s`
Maximum energy stored
`= (1)/(2) LI_(0)^(2) = (1)/(2) xx 80 xx (4)^(2) = 640 J`