An LR circuit has L = 1.0 H `R =20 Omega`. It is connected across an emf of `2.0 V at t=0`. Find `di/dt at (a) t =100ms, (b) t =200 ms and (c )t = 1.0 s`.

Explanation

Here L=1.0H,`
`R= 20 Omega, emf=2.0V`
`tau=(L/R)=(1/20)=0.05`
`i_0=e/r=2/20=0.1A`
`i_0-i_0-e^(-t//tau)`
`implies(di)/(dt)=(di_0)/(dt)-(i_0xx1-e^(-t//tau))`
`=(i_0)/(tau)e^(-t//tau)`
`So, When t=100ms`
`(di)/(dt)=(0.1)/(0.05)=e^(-0.1//0.05)=0.27 A`
`(b) When t=200ms.`
`(di)/(dt)=(0.1/0.05)xxe^(-0.2//0.05)`
`=0.0366A`
`(c ) When t=2s,(di)/(dt)=(0.1/0.5)xxe^(-0.2/0.05)`
`=41xx10^(-9)A.`