Show that the power factor of a series RLC circuit iscosϕ=RZ

Short Answer

Expert verified

We have prove that,

Power factor, cosϕ=RZ

Required proof is given below.

Step by step solution

01

Given information

We need to find out that,

Power factor is, cosϕ=RZ

02

Simplify

We know that,

Power dissipated by LCR circuit is, P=I2Zcosϕ

Here, Iis current in LCR circuit

And Zis impedance

And cosϕis power factor

Also, we know that power, P=VI

Where Vis voltage across resistor as in series voltage remain same across resistor, inductor and capacitor

Therefore, V=IR

Where Ris resistance

Therefore,

P=I2Zcosϕ=VII2Zcosϕ=IRII2Zcosϕ=I2Rcosϕ=RZ

Hence we get the require expression i.e.cosϕ=RZ

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