Reactance

This article is about electronics. For a discussion of "reactive" or "reactance" in chemistry, see reactivity.

For a discussion of the psychological concept of reactance, see reactance (psychology).

In the analysis of an alternating-current electrical circuit (for example a RLC series circuit), reactance is the imaginary part of impedance, and is caused by the presence of inductors or capacitors in the circuit. Reactance is the component of complex electric impedance of the alternating current circuit, which produces a phase shift between an electric current and voltage in the circuit. Reactance is denoted by the symbol X and is measured in ohms.

If X > 0, the reactance is said to be inductive.
If X = 0, then the circuit is purely resistive, i.e. it has no reactance.
If X < 0, it is said to be capacitive.

The relationship between impedance, resistance, and reactance is given by the equation:

[Z = R + j X \,]

where

Z is impedance, measured in ohms

R is resistance, measured in ohms

X is reactance, measured in ohms

j is the imaginary unit

Often it is enough to know the magnitude of the impedance:

[\left | Z \right | = \sqrt \,]

For a purely inductive or capacitive element, the magnitude of the impedance simplifies to just the reactance.

The reactance is given by

[X = X_L - X_C \,]

where [X_L] and [X_C] are the inductive and capacitive reactances, respectively.

Inductive reactance (symbol X_L) is caused by the fact that a current is accompanied by a magnetic field; therefore a varying current is accompanied by a varying magnetic field; the latter gives an electromotive force that resists the changes in current. The more the current changes, the more an inductor resists it: the reactance is proportional to the frequency (hence zero for DC). There is also a phase difference between the current and the applied voltage.

Inductive reactance has the formula

[X_L = \omega L = 2\pi f L \,\!]

where

X_L is the inductive reactance, measured in ohms

ω is the angular frequency, measured in radians per second

f is the frequency, measured in hertz

L is the inductance, measured in henries

Capacitive reactance (symbol X_C) reflects the fact that electrons cannot pass through a capacitor, yet effectively alternating current (AC) can: the higher the frequency the better. There is also a phase difference between the alternating current flowing through a capacitor and the potential difference across the capacitor's electrodes.

Capacitive reactance has the formula

[X_C = \frac = \frac \,]

where

X_C is the capacitive reactance measured in ohms

ω is the angular frequency, measured in radians per second

f is the frequency, measured in hertz

C is the capacitance, measured in farads

References

[1] Pohl R. W. Elektrizitätslehre. – Berlin-Gottingen-Heidelberg: Springer-Verlag, 1960.

[2] Popov V. P. The Principles of Theory of Circuits. – M.: Higher School, 1985, 496 p. (In Russian).

[3] Küpfmüller K. Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.

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Reactance

References

See also

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