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Question

State whether the given statement is True or False
In a circuit of Resistance R, self-inductance L,the current i is given by Ldidt+Ri=Ecos pt.where E and p are constants.The current i at time t is i=EL2p2+R2+[Lpsin pt+Rcos pt]+ke−Rt/L

A
True
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B
False
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Solution

The correct option is A True
Given differential equation is didt+iRL=Ecospt,
This is a Linear differential equation,
The integrating factor is,eRtL,
The solution is ieRtL=eRtL(Ecospt)dt,

Solving the integral gives,
We can solve it by Integration by parts where Ecospt=uandeRtL=v

i=EL2p2+R2+(Lpsinpt+Rcospt)+keRtL,
Where k is the integration constant.

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