A solenoid having inductance 4.0 H and resistance 10 Ω 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

`L=4.0H, R=10 (Omega), E=4V`
`(a) Time constant ,
`(tau)=(L/R)=(4/10)0.4s`
`(b) i=0.63 (I_0)`
`Now 0.63 (I_0)= (I_0)(1-e^(-t//(tau))`
`impliese^(-t//(tau))=1.063=0.37`
`In(e^(-t//(tau))=In0.037`
`implies -(t/(tau))=-0.9942`
`impliest=0.642xx0.04`
`(c ) i=i_0(1-e^(-t//(tau))`
`=(4/10)(1-e^(-0.4//0.04)`
`=0.4xx0.6321`
`=0.2526A`
power delivered
`P=V_(i)=4xx0.2528`
`=1.01=1W`
(d) Power dissipated in Joule heating
`=1^2R=(0.2258)^2xx10`
`0.639=0.64W`.