A solenoid having inductance 4.0 H and resistance `10 Omega` is connected to a 4.0 V battery at t = 0. Find (a) the time constant, (b) the time elapsed before the current reached 0.63 of its steady state value, (c ) the power delivered by the battery at this instant and (d) the power dissipated in Joule heating at this instant.

Explanation

Steady-state current `i_(0)=(E)/(R)=(4)/(10)=0.4A`
(a) `tau=(L)/(R)=(4)/(10)=0.4sec`
(b) `i=i_(0)(1-e^(-t//tau))`
`-(t)/(tau)1n e=1n(0.37)=-1`
`t=tau=0.4sec`
When `i=0.63i_(0)`
`P=Ei=E(0.63i_(0))=4xx0.63xx0.4`
`=1W`
(d) `P'=i^(2)R=(0.63i_(0))^(2)xx10=0.64W`