In an L-R-C series circuit, what are the phase angle$\mathit{\varphi }$and power factor cos$\mathit{\varphi }$when the resistance is much smaller than the inductive or capacitive reactance and the circuit is operated far from resonance? Explain.

An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. When an inductor is attached to an AC supply, the resistance produced by it is called inductive reactance (X_L).

A capacitor is a two-terminal device that stores energy in a electric field when current passes through it. When a capacitor is attached to an AC supply, the resistance produced by it is called capacitive reactance (X_C).

Resistance is measure of opposition to the flow of current in a closed electrical circuit. It is measured in Ohm (Ω).

Impedance is defined as the effective resistance of an electric circuit to the flow of current due to the combined effect of resistance (offered by resistor) and reactance (offered by capacitor and inductor).

Power factor of an AC circuit is defined as the ratio of real power absorbed to the apparent power flowing in the AC circuit. It is a dimensionless quantity and its value lies in the interval [-1,1].

The power factor is given by the relation:

$\cos \varphi =\frac{R}{\sqrt{R^2}{\left(\omega L-{\displaystyle \frac{1}{\omega C}}\right)}^2}$

When resistance is very small compared to inductive and capacitive reactance and the frequency is far from resonance frequency,

$$\begin{gathered} R<<<<<<X_L \\ R<<<<<<X_C \\ \omega L-\frac{1}{\omega C}\ne 0 \end{gathered}$$

Therefore, the power factor $\mathbf{\left(}\mathbf{cos\varphi }\mathbf{\right)}$is nearly zero that makes phase angle, ϕ = 90°.