Reactance

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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 produces a phase shift between the 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 in ohms,

R is resistance in ohms,

X is reactance in ohms,

and j is the imaginary unit $\sqrt{-1}$ .

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

$\left | Z \right | = \sqrt {R^2 + X^2} \,$

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

The reactance of an inductor and a capacitor in series is the algebraic sum of their reactances:

$X = X_L + X_C \,$

where $X L$ and $X C$ are the inductive and capacitive reactances, which are positive and negative, 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

$X_C = -\frac {1} {\omega C} = -\frac {1} {2\pi f C} \,$

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

[edit] References

Pohl R. W. Elektrizitätslehre. – Berlin-Gottingen-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.
Young, Hugh D.; Roger A. Goodman and A. Lewis Ford [1949] (2004). Sears and Zemansky's University Physics, 11 ed, San Francisco: Addison Wesley. ISBN 0-8053-9179-7. Retrieved on September 30, 2006.