Reactance

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Reactance (German: Blindwiderstand, also Reaktanz) describes the frequency-dependent resistance of inductors and capacitors with alternating current. Unlike ohmic resistance, reactance leads to a phase difference between voltage and current without converting energy into heat.

In the fundamentals of electrical engineering (EE1) only for completeness

This quantity appears in the EE1 script only for the sake of completeness, because it belongs to the components inductor and capacitor. Calculations and a deeper understanding are part of alternating current theory (EE2).

1 Quantity symbol and unit

The quantity symbol of reactance is $X$.
Its unit is the ohm with the unit symbol $\Omega$.

$$[X]=\Omega$$

A distinction is made between:

• Inductive reactance $X_L$: reactance of an inductor
• Capacitive reactance $X_C$: reactance of a capacitor
• Total reactance $X=X_L-X_C$

2 Practical and worked examples

2.1 Inductive reactance of an inductor

Inductive reactance increases linearly with frequency:

$$X_L=\omega L=2\pi fL$$

Example: inductance $L=10\mathrm{mH}$, frequency $f=1\mathrm{kHz}$

$$X_L=2\pi \cdot 1000\mathrm{Hz}\cdot 10\cdot 10^{-3}\mathrm{H}=\underline{62.8\mathrm{\Omega }}$$

At $f=10\mathrm{kHz}$:

$$X_L=2\pi \cdot 10000\mathrm{Hz}\cdot 10\cdot 10^{-3}\mathrm{H}=\underline{628\mathrm{\Omega }}$$

2.2 Capacitive reactance of a capacitor

Capacitive reactance decreases in inverse proportion to frequency:

$$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}$$

Example: capacitance $C=100\mathrm{nF}$, frequency $f=1\mathrm{kHz}$

$$X_C=\frac{1}{2\pi \cdot 1000\mathrm{Hz}\cdot 100\cdot 10^{-9}\mathrm{F}}=\underline{1.59\mathrm{k\Omega }}$$

At $f=10\mathrm{kHz}$:

$$X_C=\frac{1}{2\pi \cdot 10000\mathrm{Hz}\cdot 100\cdot 10^{-9}\mathrm{F}}=\underline{159\mathrm{\Omega }}$$

2.3 Resonance frequency

At the resonance frequency, the inductive and capacitive reactance of an LC resonant circuit are equal:

$$X_L=X_C\Rightarrow f_0=\frac{1}{2\pi \sqrt{LC}}$$

Example: $L=10\mathrm{mH}$, $C=100\mathrm{nF}$

$$f_0=\frac{1}{2\pi \sqrt{10\cdot 10^{-3}\mathrm{H}\cdot 100\cdot 10^{-9}\mathrm{F}}}=\underline{5.03\mathrm{kHz}}$$

Unit check:

$$[f_0]=\frac{1}{\sqrt{[L][C]}}=\frac{1}{\sqrt{\mathrm{H}\cdot \mathrm{F}}}=\frac{1}{\sqrt{\frac{\mathrm{V}\cdot \mathrm{s}}{\mathrm{A}}\cdot \frac{\mathrm{A}\cdot \mathrm{s}}{\mathrm{V}}}}=\frac{1}{\sqrt{{\mathrm{s}}^2}}=\frac{1}{\mathrm{s}}=\mathrm{Hz}$$

3 Typical orders of magnitude

• Inductive reactance at 50 Hz: $1\mathrm{\Omega }$ to $1\mathrm{k\Omega }$ (depending on the inductance)
• Capacitive reactance at 50 Hz: $100\mathrm{\Omega }$ to $100\mathrm{k\Omega }$ (depending on the capacitance)
• RF circuits: $1\mathrm{\Omega }$ to $1\mathrm{k\Omega }$
• Mains filters: $10\mathrm{\Omega }$ to $10\mathrm{k\Omega }$

4 Example phrasings

• ‘The inductive reactance of the inductor at 1 kHz is exactly $62.8\mathrm{\Omega }$.’
• ‘At 50 Hz, the capacitor has a capacitive reactance of $3.2\mathrm{k\Omega }$.’
• ‘At the resonance frequency of 5 kHz, inductive and capacitive reactance cancel each other out.’
• ‘The total reactance of the electric circuit is $X=X_L-X_C=150\mathrm{\Omega }$ (inductive).’

5 Related quantities

• Impedance from resistance and reactance:

$$Z=R+jX=R+j(X_L-X_C)$$

• Inductive reactance:

$$X_L=\omega L=2\pi fL$$

• Capacitive reactance:

$$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}$$

• Angular frequency:

$$\omega =2\pi f$$

• Resonance frequency:

$$f_0=\frac{1}{2\pi \sqrt{LC}}$$

6 Related components

• Inductor: produces inductive reactance, which increases with frequency
• Capacitor: produces capacitive reactance, which decreases with frequency
• Transformer: leakage inductances cause inductive reactance