An AC voltage $V = V_m$ is applied across a:
- Series RC circuit in which capacitive reactance is ‘a’ times the resistance in the circuit.
- Series RL circuit in which inductive reactance is ‘b’ times the resistance in the circuit.
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Power factor $\cos\varphi=\frac{\text{R}}{\text{Z}},$ when $\text{Z}=\sqrt{\text{R}^2+\text{X}^2}$
$\therefore\cos\varphi=\frac{\text{R}}{\text{R}\sqrt{1+\text{a}^2}}=\frac{1}{\sqrt{1+\text{a}^2}}$
$\therefore\cos\varphi=\frac{\text{R}}{\text{R}\sqrt{1+\text{b}^2}}=\frac{1}{\sqrt{1+\text{b}^2}}$
- $\text{X = X}_{\text{C}} = \text{aR},$
$\therefore\cos\varphi=\frac{\text{R}}{\text{R}\sqrt{1+\text{a}^2}}=\frac{1}{\sqrt{1+\text{a}^2}}$
- $\text{X = X}_{\text{L}}=\text{bR},$
$\therefore\cos\varphi=\frac{\text{R}}{\text{R}\sqrt{1+\text{b}^2}}=\frac{1}{\sqrt{1+\text{b}^2}}$
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