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=Ecospt.where E and p are constants.The current i at time t is i=EL2p2+R2+[Lpsinpt+Rcospt]+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=uande−RtL=v