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The circuit is switched on at t=0, Find ...

The circuit is switched on at `t=0`, Find the time when energy stored in inductor becomes `1/n` tiimes of maximum energy stored in it:

A

`L/Rln((sqrtn)/(sqrtn-1))`

B

`L/Rln((sqrtn+1)/(sqrtn-1))`

C

`L/Rln((sqrtn)/(sqrtn+1))`

D

`L/Rln((sqrtn-1)/(sqrtn))`

Text Solution

Verified by Experts

The correct Answer is:
A
`U_(max)=1/2LI^2max`
`i=I_(max)(1-e^(-Rt//L))`
For U to be `(U_(max))/n` , i has to be `I_("max")/sqrtn`
`I_(max)/sqrtn=I_(max)(1-e^(Rt//L))`
`e^(-Rt//L)=1-1/sqrtn=(sqrtn-1)/sqrtn`
`-(Rt)/L=ln(sqrtn-1)/sqrtn`
`t=L/R ln ((sqrtn)/(sqrtn-1))`
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