MP Board · Class 12 · Physics · Alternating CurrentExplain the concept of 'Wattless Current' in an alternating current (AC) circuit. Under what condition is the current in an AC circuit said to be purely wattless?

In an alternating current (AC) circuit, the average power dissipated per cycle is given by the formula: $$P = V_{rms} I_{rms} \cos\phi$$\nwhere $V_{rms}$ is the root-mean-square voltage, $I_{rms}$ is the root-mean-square current, and $\cos\phi$ is the power factor of the circuit, with $\phi$ being the phase angle between voltage and current. \nWhen a circuit contains only a pure inductor ($L$) or a pure capacitor ($C$), the phase difference between the alternating voltage and alternating current is $\phi = \frac{\pi}{2}$ radians or $90^\circ$. \nSubstituting this into the power formula: $$\cos\left(\frac{\pi}{2}\right) = 0 \implies P = 0$$ \nThis means that even though current flows through the circuit, the average power consumed by the circuit over a full cycle is zero. This current, which flows without consuming any electrical energy, is called Wattless Current. \nIn general, the component of current $I_{rms} \sin\phi$ which is perpendicular to the voltage component in a phasor diagram is called the wattless component of current.