Editing Phasor (section)

=== Circuit laws ===

With phasors, the techniques for solving [[direct current|DC]] circuits can be applied to solve linear AC circuits.{{Efn|name="ac-circuits"}}

; Ohm's law for resistors: A [[resistor]] has no time delays and therefore doesn't change the phase of a signal therefore {{math|1=''V'' = ''IR''}} remains valid.
; Ohm's law for resistors, inductors, and capacitors: {{math|1=''V'' = ''IZ''}} where {{mvar|Z}} is the complex [[electrical impedance|impedance]].<!-- we probably want a justification of this somewhere-->
; [[Kirchhoff's circuit laws]]: Work with voltages and current as complex phasors.

In an AC circuit we have real power ({{mvar|P}}) which is a representation of the average power into the circuit and reactive power (''Q'') which indicates power flowing back and forth. We can also define the [[complex power]] {{math|1=''S'' = ''P'' + ''jQ''}} and the apparent power which is the magnitude of {{mvar|S}}. The power law for an AC circuit expressed in phasors is then {{math|1=''S'' = ''VI''<sup>*</sup>}} (where {{math|1=''I''<sup>*</sup>}} is the [[complex conjugate]] of {{math|1=''I''}}, and the magnitudes of the voltage and current phasors {{math|1=''V''}} and of {{math|1=''I''}} are the [[Root mean square#Definition|RMS]] values of the voltage and current, respectively).

Given this we can apply the techniques of [[analysis of resistive circuits]] with phasors to analyze single frequency linear AC circuits containing resistors, capacitors, and [[inductor]]s. Multiple frequency linear AC circuits and AC circuits with different waveforms can be analyzed to find voltages and currents by transforming all waveforms to sine wave components (using [[Fourier series]]) with magnitude and phase then analyzing each frequency separately, as allowed by the [[superposition theorem]]. This solution method applies only to inputs that are sinusoidal and for solutions that are in steady state, i.e., after all transients have died out.<ref>{{Cite book|title=Introduction to electromagnetic compatibility| last=Clayton|first=Paul| publisher=Wiley|year=2008|isbn=978-81-265-2875-2|pages=861}}</ref>

The concept is frequently involved in representing an [[electrical impedance]]. In this case, the phase angle is the [[phase difference]] between the voltage applied to the impedance and the current driven through it.