Phasors

A sinusoid $V_m\cos(\omega t + \phi)$ at a known frequency is represented by the phasor:

$\mathbf{V} = V\angle\phi = V(\cos\phi + j\sin\phi)$

(usually with RMS magnitude in power engineering). Differentiation becomes multiplication by $j\omega$, so the differential equations of AC circuits become algebra.

• Rectangular form $a + jb$ — easy to add.
• Polar form $r\angle\theta$ — easy to multiply and divide.

A phasor diagram shows the relative phase of voltages and currents at a glance.