Physics » Electromagnetic Induction and AC Circuits » Reactance, Inductive and Capacitive

# 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 $${X}_{C}=\cfrac{1}{2\pi \text{fC}}$$