Question

A series RLC circuit has a resistance of 54.33 ohm, a capacitance of 2.56 microF, and an inductance of 172.91 mH. The circuit is connected to a variable-frequency source with a fixed rms output of 54.03 V. The frequency is 60 Hz.• Determine the power factor.

Answer 1

Given:

R = 54.33 Ohm

C = 2.56 micro F

L = 172.91 mH

f = 60 Hz

To find:

The power factor.

Explanation:

The inductive reactance can be calculated as:

$X_L=2\pi fL=2\pi\times60\times172.91\times10^{-3}=65.1855\text{ Ohm}$

The capacitive reactance can be calculated as:

$X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi\times60\times2.56\times10^{-6}}=\frac{1}{9.6509\times10^{-4}}=1036.172\text{ Ohm}$

The phase angle is given as:

$\varphi=tan^{-1}(\frac{X_L-X_C}{R})=tan^{-1}(\frac{65.1855-1036.172}{54.06})=-86.81\degree$

The power factor is given as:

$P.F=cos\varphi=cos(-86.81\degree)=0.0556$

Final answer:

The power factor is 0.0556.