Question

derive expression for irms​

Answer 1

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Solution:-

Average power in LCR circuit:-

let V=V0sinωtthenI=I0sinωt−ϕ

where, ϕ = phase angle

Total work done over complete cycle:-

W=∫0TVIdt

=∫0TV0sinωt.I0sinωt−ϕdt

=2V0I0∫0T2sinωt.sinωt−ϕdt

Using this

2sinA.sinB=cos(A−B)−cos(A+B)

we get

W=2V0I0∫0T[cosϕ−cos(2ωt−ϕ)]dt

W=2V0I0[Tcosϕ]

TW=2V0