## Summary

- The AC analogy to resistance is impedance \(Z\), the combined effect of resistors, inductors, and capacitors, defined by the AC version of Ohm’s law:
\({I}_{0}=\cfrac{{V}_{0}}{Z}\phantom{\rule{0.25em}{0ex}}\text{or}\phantom{\rule{0.25em}{0ex}}{I}_{\text{rms}}=\cfrac{{V}_{\text{rms}}}{Z},\)

where \({I}_{0}\) is the peak current and \({V}_{0}\) is the peak source voltage.

- Impedance has units of ohms and is given by \(Z=\sqrt{{R}^{2}+({X}_{L}-{X}_{C}{)}^{2}}\).
- The resonant frequency \({f}_{0}\), at which \({X}_{L}={X}_{C}\), is
\({f}_{0}=\cfrac{1}{2\pi \sqrt{\text{LC}}}\text{.}\)

- In an AC circuit, there is a phase angle
*\(\varphi \)*between source voltage \(V\) and the current \(I\), which can be found from\(\text{cos}\phantom{\rule{0.25em}{0ex}}\varphi =\cfrac{R}{Z}\text{,}\)

- \(\varphi =0º\) for a purely resistive circuit or an
*RLC*circuit at resonance. - The average power delivered to an
*RLC*circuit is affected by the phase angle and is given by\({P}_{\text{ave}}={I}_{\text{rms}}{V}_{\text{rms}}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\varphi \text{,}\)

\(\text{cos}\phantom{\rule{0.25em}{0ex}}\varphi \) is called the power factor, which ranges from 0 to 1.

## Glossary

### impedance

the AC analogue to resistance in a DC circuit; it is the combined effect of resistance, inductive reactance, and capacitive reactance in the form \(Z=\sqrt{{R}^{2}+({X}_{L}-{X}_{C}{)}^{2}}\)

### resonant frequency

the frequency at which the impedance in a circuit is at a minimum, and also the frequency at which the circuit would oscillate if not driven by a voltage source; calculated by \({f}_{0}=\cfrac{1}{2\pi \sqrt{\text{LC}}}\)

### phase angle

denoted by *\(\varphi \)*, the amount by which the voltage and current are out of phase with each other in a circuit

### power factor

the amount by which the power delivered in the circuit is less than the theoretical maximum of the circuit due to voltage and current being out of phase; calculated by \(\text{cos}\phantom{\rule{0.25em}{0ex}}\varphi \)