Question

Calculate the power factor of this circuit and compare this value with one at its resonant frequency.

Answer 1

We know that the power factor of LCR circuit is given as

$\cos \varphi =\frac{R}{Z}$

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

$X_L=2\pi fL$

$X_L=200\Omega$

$X_C=\frac{1}{2\pi fC}$

$X_C=\frac{1}{2\times 50\times 100}\Omega$

$Z=\sqrt{{100}^2+{\left(200-\frac{1}{10000}\right)}^2}$

The power factor is,

$\cos \varphi =\frac{100}{\sqrt{10000+39960}}$

$\varphi ={\cos }^{-1}\left(0.447\right)$

$={63.4}^{\circ }$

$=1.105rad$

At resonance, the inductive reactance is equal to capacitive reactance and they cancel out each other. So, the power factor at resonance is unity. Thus,

$\varphi =1.105{\varphi }_{resonance}$