Explanation

(b) As, power factor $= \frac{true\ power}{apparent\ power}$
$= \cos\phi$
$= \frac{R}{\sqrt{R^{2} + \left( X_{L} - X_{C} \right)^{2}}}$
$\therefore$ power factor$= \cos{\phi = \frac{R}{Z}}$
In a non-inductive circuit, $X_{L} = X_{C}$
$\therefore\ \ \ \ \ \ \ \ \ Power\ factor = \cos{\phi = \frac{R}{\sqrt{R^{2}}}} = \frac{R}{R} = 1$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \phi = 0{^\circ}$
This is the maximum value of power factor. In a pure inductor or an ideal capacitor
$\phi = 90{^\circ}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $Power factor$= \cos{\phi = \cos{90{^\circ} = 0}}\ $
Average power consumed in a pure inductor or ideal capacitor
$P = E_{v}.I_{v}\cos{90{^\circ} = zero}$
Therefore, current through pure L or pure C, which consumes no power for its maintenance in the circuit is called ideal current or wattles current.