Summarizing Reactance, Inductive and Capacitive

Summary

• For inductors in AC circuits, we find that when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one-fourth of a cycle, or by a \(\text{90º}\) phase angle.
• The opposition of an inductor to a change in current is expressed as a type of AC resistance.
• Ohm’s law for an inductor is

  \(I=\cfrac{V}{{X}_{L}}\text{,}\)

  where \(V\) is the rms voltage across the inductor.
• \({X}_{L}\) is defined to be the inductive reactance, given by

  \({X}_{L}=2\pi \text{fL}\text{,}\)

  with \(f\) the frequency of the AC voltage source in hertz.
• Inductive reactance \({X}_{L}\) has units of ohms and is greatest at high frequencies.
• For capacitors, we find that when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle, or by a \(\text{90º}\) phase angle.
• Since a capacitor can stop current when fully charged, it limits current and offers another form of AC resistance; Ohm’s law for a capacitor is

  \(I=\cfrac{V}{{X}_{C}}\text{,}\)

  where \(V\) is the rms voltage across the capacitor.
• \({X}_{C}\) is defined to be the capacitive reactance, given by

  \({X}_{C}=\cfrac{1}{2\pi \text{fC}}\text{.}\)

• \({X}_{C}\) has units of ohms and is greatest at low frequencies.

Glossary

inductive reactance

the opposition of an inductor to a change in current; calculated by \({X}_{L}=2\pi \text{fL}\)

capacitive reactance

the opposition of a capacitor to a change in current; calculated by \({X}_{C}=\cfrac{1}{2\pi \text{fC}}\)