Question on topic in Chelapati book

[cbinla]

Ok I'm starting to go through the Chelapati book and stuck on a formula given. In discussing how to represent a simple load with a resistance and reactance in series, the formula for Rs is given as Rs = (V^2 cos theta)/S. Cosine theta is in the numerator.

I could just accept this formula, but I'd like to understand it more by deriving it and I'm stuck. If I start with the basic formula P = V^2 / Rs and use the definition of PF = P/S (real power divided by apparent power), I should be able to substitute S*PF for P and solve for R, but when I do this I get cos theta in the denominator, Rs = V^2 / (S*cos theta). Can anyone help tell me where my mistake or incorrect assumption is please?

Thank you

 

[GabeM]

Ok I'm starting to go through the Chelapati book and stuck on a formula given. In discussing how to represent a simple load with a resistance and reactance in series, the formula for Rs is given as Rs = (V^2 cos theta)/S. Cosine theta is in the numerator.
I could just accept this formula, but I'd like to understand it more by deriving it and I'm stuck. If I start with the basic formula P = V^2 / Rs and use the definition of PF = P/S (real power divided by apparent power), I should be able to substitute S*PF for P and solve for R, but when I do this I get cos theta in the denominator, Rs = V^2 / (S*cos theta). Can anyone help tell me where my mistake or incorrect assumption is please?

Thank you

The basic formula you are starting with is incorrect. The correct formula is S = V^2 / Rs. Substituting PF = P/S into this formula will give Rs = (V^2 cos theta)/S.

 

[cdcengineer]

Let me take a crack..

Try this - V*cos theta=V®=IR

Where V sub R or V® is the voltage across the resistive component of the series equivalent form of the load impedance.

or

P=IV*cos theta=I*V®=I^2*R in watts