Question

Use Eq. cosϕ=R/Z to show that the average power delivered by the source in an L−R−C series circuit is given by Pav = I^2rmsR .

Answer 1

Step-by-step explanation:

In a L C R circuit, the average power is given by

`P_(av)=V_(rms)I_(rms)Cos\phi`

As given in the question

CosФ = R / Z

And we know that

`V_(rms)=I_(rms)* Z`

So

`P_(av)=I_(rms)* Z* I_(rms)* (R)/(Z)`

`P_(av)=I_(rms)^(2)* R`