AC circuits. Ohm's law for resistors A resistor has no time delays and therefore doesn't change the phase of a signal therefore remains valid. Ohm's law for resistors, inductors, and capacitors where is the complex impedance. Kirchhoff's circuit laws Work with voltages and current as complex phasors. In an AC circuit we have real power () 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 and the apparent power which is the magnitude of . The power law for an AC circuit expressed in phasors is then (where is the complex conjugate of , and the magnitudes of the voltage and current phasors and of are the 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 inductors. 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. 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. Power engineering In analysis of three phase AC power systems, usually a set of phasors is defined as the three complex cube roots of unity, graphically represented as unit magnitudes at angles of 0, 120 and 240 degrees. By treating polyphase AC circuit quantities as phasors, balanced circuits can be simplified and unbalanced circuits can be treated as an algebraic combination of symmetrical components. This approach greatly simplifies the work required in electrical calculations of voltage drop, power flow, and short-circuit currents. In the context of power systems analysis, the phase angle is often given in degrees, and the magnitude in RMS value rather than the peak amplitude of the sinusoid. The technique of synchrophasors uses digital instruments to measure the phasors representing transmission system voltages at widespread points in a transmission network. Differences among the