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Question

State whether the following statement is True or False.
The current in the circuit with inductance L and resistance R and voltage Esinωt is given by Ldidt+Ri=Esinωt.if i=0 at t=0 then,current is given by i=EE2+L2ω2[sin(ωtϕ)+eRt/Lsinϕ] where ϕ=tan1(LωR)

A
True
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B
False
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Solution

The correct option is A True
The differential equation is didt+iRL=EsinωtL,

This is linear differential equation,
The integrating factor is eRtL,
The solution is ieRtL=eRtLEsinωtdt,

The integral can be solved by using integration by parts,
where u=Esinωtandv=eRtL,

The solution is i=EE2+L2ω2sin(ωtϕ)+eRtLwhereϕ=tan1LωR

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