Wattless Current

Consider an AC circuit in which there is a phase angle $\phi$ between $V_{RMS}$ and $I_{RMS}$, with voltage leading current (as in a phasor diagram where $V_{RMS}$ sits an angle $\phi$ ahead of $I_{RMS}$). Resolving $I_{RMS}$ into two perpendicular components relative to the direction of $V_{RMS}$ gives one component $I_{RMS}\cos\phi$, lying ALONG (parallel to) $V_{RMS}$, and a second component $I_{RMS}\sin\phi$, PERPENDICULAR to $V_{RMS}$.

The component $I_{RMS}\cos\phi$ IN PHASE with the voltage is called the active component: the power it delivers is $V_{RMS}I_{RMS}\cos\phi$, exactly matching the average power formula of section 4.8.1, so this component is also called the 'wattful' current -- it is the only part of the total current that does any genuine, useful electrical work. The other component, $I_{RMS}\sin\phi$, has a $90^{\circ}$ ($\pi/2$) phase angle relative to the voltage, and is called the reactive component; because power averaged over a cycle for a $90^{\circ}$-phase-shifted voltage-current pair is always exactly zero (using $\cos90^{\circ}=0$ in the average-power formula), this component delivers zero net power, and is accordingly called the 'wattless' current. …