MP Board · Class 12 · Physics · Alternating CurrentWhat is meant by Wattless Current? Under what conditions does the current in an AC circuit become wattless?

Wattless Current:\nWattless current is defined as that component of alternating current in an AC circuit which consumes zero average power over a complete cycle. When current flows through a circuit without causing any dissipation of electric energy in the form of heat, it is called wattless current.

Mathematical Derivation & Conditions:\nThe average power consumed in an AC circuit is given by: $$P_{avg} = V_{rms} I_{rms} \cos\phi$$\nwhere $\cos\phi$ is the power factor and $\phi$ is the phase angle between voltage and current. \nFor power consumed to be zero ($P_{avg} = 0$), we must have: $$\cos\phi = 0 \implies \phi = 90^\circ = \frac{\pi}{2}\text{ radians}$$

Conditions for Wattless Current:

1. Purely Inductive Circuit: In a circuit containing only a pure inductor ($L$), the current lags behind the voltage by a phase angle of $90^\circ$ ($\phi = 90^\circ$). Thus, $P_{avg} = 0$.
2. Purely Capacitive Circuit: In a circuit containing only a pure capacitor ($C$), the current leads the voltage by a phase angle of $90^\circ$ ($\phi = 90^\circ$). Thus, $P_{avg} = 0$.
3. Resistance ($R$) in the circuit must be zero (ideal non-resistive circuit).