Question

A 60 cycle AC circuit has a resistance of 200 om and inductor of 100mH. What capacitance placed in the circuit will make the power factor unity?

Answer 1

Power factor, 

\(\cos\theta = \frac RZ \)

\(= \frac{200}{203.52}\)

\(= 0.983\)

Now, for the power factor to be unit, ϕ = 0 that means

\(X_L = X_C\) or \(\omega L= 1(\omega C)\)

\(\therefore C = \frac 1{(\omega)^2L}\)

\(= \frac 1{(2\pi60)^2 \times 100 \times 10^{-3}}\)

\(\therefore \) C = 70.36 µF