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In the following circuit the switch is c...

In the following circuit the switch is closed at `t=0`.Intially there is no current in inductor.Find out current the inductor coil as a function of time.

Text Solution

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At any time t
`-epsi+i_(1)R-(i-i_(1))R=0`
`-epsi+2i_(1)R-iR=0`
`i_(1)=(iR+epsi)/(2R) " Now," -epsi+i_(1)R+iR+L.(di)/(dt)=0`
`=epsi+((iR+epsi)/(2))+iR+L.(di)/(dt)=0 " " implies =(epsi)/(2)+(3iR)/(2)= -L.(di)/(dt)`
`((-epsi+3iR)/(2))dt=-L.di" "implies-(-dt)/(2L)=(di)/(-epsi+3iR)`
`-int_(0)^(t)(dt)/(2L)=int_(0)^(i)(di)/(-epsi+3iR) " " implies -(t)/(2L)=(1)/(3R)In ((-epsi+3iR)/(-epsi))`
`-In((-epsi+3iR)/(-epsi))=(3Rt)/(2L)" "implies i=+(epsi)/(3R)(1-e^(-(3Rt)/(2L)))`
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