### Reactance (electronics)

In electrical and electronic systems, **reactance** is the opposition of a circuit element to a change of electric current or voltage, due to that element's inductance or capacitance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current. The notion of reactance is similar to electrical resistance, but they differ in several respects.

An ideal resistor has zero reactance, while ideal inductors and capacitors consist entirely of reactance, having zero and infinite resistance respectively.

## Contents

## Analysis

In phasor analysis, reactance is used to compute amplitude and phase changes of sinusoidal alternating current going through the circuit element. It is denoted by the symbol $\backslash scriptstyle\{X\}$.

Both reactance $\backslash scriptstyle\{X\}$ and resistance $\backslash scriptstyle\{R\}$ are components of impedance $\backslash scriptstyle\{Z\}$.

- $Z\; =\; R\; +\; jX\backslash ,$

- where

- $\backslash scriptstyle\{Z\}$ is the impedance, measured in ohms.
- $\backslash scriptstyle\{R\}$ is the resistance, measured in ohms.
- $\backslash scriptstyle\{X\}$ is the reactance, measured in ohms.
- $\backslash scriptstyle\; j\; \backslash ;=\backslash ;\; \backslash sqrt\{-1\}$

Both capacitive reactance $\backslash scriptstyle\{X\_C\}$ and inductive reactance $\backslash scriptstyle\{X\_L\}$ contribute to the total reactance $\backslash scriptstyle\{X\}$.

- $\{X\; =\; X\_L\; -\; X\_C\; =\; \backslash omega\; L\; -\backslash frac\; \{1\}\; \{\backslash omega\; C\}\}$

- where

- $\backslash scriptstyle\{X\_C\}$ is the capacitive reactance, measured in ohms
- $\backslash scriptstyle\{X\_L\}$ is the inductive reactance, measured in ohms

Although $\backslash scriptstyle\{X\_L\}$ and $\backslash scriptstyle\{X\_C\}$ are both positive by convention, the capacitive reactance $\backslash scriptstyle\{X\_C\}$ makes a negative contribution to total reactance.

Hence,

- If $\backslash scriptstyle\; X\; \backslash ;>\backslash ;\; 0$, the reactance is said to be inductive.
- If $\backslash scriptstyle\; X\; \backslash ;=\backslash ;\; 0$, then the impedance is purely resistive.
- If $\backslash scriptstyle\; X\; \backslash ;<\backslash ;\; 0$, the reactance is said to be capacitive

## Capacitive reactance

**Capacitive reactance** is an opposition to the change of voltage across an element. Capacitive reactance $\backslash scriptstyle\{X\_C\}$ is inversely proportional to the signal frequency $\backslash scriptstyle\{f\}$ (or angular frequency ω) and the capacitance $\backslash scriptstyle\{C\}$.^{[1]}

- $X\_C\; =\; \backslash frac\; \{1\}\; \{\backslash omega\; C\}\; =\; \backslash frac\; \{1\}\; \{2\backslash pi\; f\; C\}$
^{[2]}

A capacitor consists of two conductors separated by an insulator, also known as a dielectric.

At low frequencies a capacitor is open circuit, as no current flows in the dielectric. A DC voltage applied across a capacitor causes positive charge to accumulate on one side and negative charge to accumulate on the other side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero.

Driven by an AC supply, a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge dissipates. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.

## Inductive reactance

**Inductive reactance** is an opposition to the change of current on an inductive element. Inductive reactance $\backslash scriptstyle\{X\_L\}$ is proportional to the sinusoidal signal frequency $\backslash scriptstyle\{f\}$ and the inductance $\backslash scriptstyle\{L\}$.

- $X\_L\; =\; \backslash omega\; L\; =\; 2\backslash pi\; f\; L$

The average current flowing in an inductance $\backslash scriptstyle\{L\}$ in series with a sinusoidal AC voltage source of RMS amplitude $\backslash scriptstyle\{A\}$ and frequency $\backslash scriptstyle\{f\}$ is equal to:

- $I\_L\; =\; \{A\; \backslash over\; \backslash omega\; L\}\; =\; \{A\; \backslash over\; 2\backslash pi\; f\; L\}$

The average current flowing in an inductance $\backslash scriptstyle\{L\}$ in series with a square wave AC voltage source of RMS amplitude $\backslash scriptstyle\{A\}$ and frequency $\backslash scriptstyle\{f\}$ is equal to:

- $I\_L\; =\; \{A\; \backslash pi^2\; \backslash over\; 8\; \backslash omega\; L\}\; =\; \{A\backslash pi\; \backslash over\; 16\; f\; L\}$ making it appear as if the inductive reactance to a square wave was $X\_L\; =\; \{16\; \backslash over\; \backslash pi\}\; f\; L$

An inductor consists of a coiled conductor. Faraday's law of electromagnetic induction gives the counter-emf $\backslash scriptstyle\{\backslash mathcal\{E\}\}$ (voltage opposing current) due to a rate-of-change of magnetic flux density $\backslash scriptstyle\{B\}$ through a current loop.

- $\backslash mathcal\{E\}\; =\; -\backslash right)\; =\; -jX\_C\; \backslash \backslash \; \backslash tilde\{Z\}\_L\; \&=\; \backslash omega\; Le^\{j\{\backslash pi\; \backslash over\; 2\}\}\; =\; j\backslash omega\; L\; =\; jX\_L\backslash quad$
\end{align}

For a reactive component the sinusoidal voltage across the component is in quadrature (a $\backslash scriptstyle\{\backslash pi/2\}$ phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power.

## See also

## References

- Pohl R. W.
*Elektrizitätslehre.*– Berlin-Göttingen-Heidelberg: Springer-Verlag, 1960. - Popov V. P.
*The Principles of Theory of Circuits.*– M.: Higher School, 1985, 496 p. (In Russian). - Küpfmüller K.
*Einführung in die theoretische Elektrotechnik,*Springer-Verlag, 1959. -

## External links

- Interactive Java Tutorial on Inductive Reactance National High Magnetic Field Laboratoryhe:עכבה חשמלית#היגב

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