In electrical and electronic systems, reactance is the opposition of a circuit
element to a change in 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 it differs in
several respects. In phasor analysis, reactance is used to
compute amplitude and phase changes of sinusoidal alternating current going
through a circuit element. It is denoted by the symbol . An ideal resistor has
zero reactance, whereas ideal inductors and capacitors have zero resistance –
that is, respond to current only by reactance. The magnitude of the
reactance of an inductor rises in proportion to a rise in frequency, while
the magnitude of the reactance of a capacitor decreases in proportion to a
rise in frequency. As frequency goes up, inductive reactance goes up and
capacitive reactance goes down. Capacitive reactance
Capacitive reactance is an opposition to the change of voltage across an element.
Capacitive reactance is inversely proportional to the signal frequency
and the capacitance . A capacitor consists of two conductors
separated by an insulator, also known as a dielectric.
At low frequencies a capacitor is an open circuit so 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 through an element. Inductive reactance is
proportional to the sinusoidal signal frequency and the inductance .
The average current flowing through an inductance in series with a sinusoidal
AC voltage source of RMS amplitude and frequency is equal to:
Because a square wave has multiple amplitudes at sinusoidal harmonics, the
average current flowing through an inductance in series with a square wave
AC voltage source of RMS amplitude and frequency is equal to:
making it appear as if the inductive reactance to a square wave was about 19%
smaller than the reactance to the AC sine wave:
Any conductor of finite dimensions has inductance; the inductance is made
larger by the multiple turns in an electromagnetic coil. Faraday's law of
electromagnetic induction gives the counter-emf due to a rate-of-change of
magnetic flux density through a current loop.
For an inductor consisting of a coil with loops this gives.
The counter-emf is the source of the opposition to current flow. A constant
direct current has a zero rate-of-change, and sees an inductor as
a short-circuit. An alternating current has a time-averaged rate-of-change that
is proportional to frequency, this causes the increase in inductive
reactance with frequency. Impedance
Both reactance and resistance are components of impedance .
where: is the impedance, measured in ohms;
is the resistance, measured in ohms. It is the real part of the impedance:
is the reactance, measured in ohms. It is the imaginary part of the impedance:
is the square root of minus one, usually represented by in non-electrical
formulas. When both a capacitor and an inductor
are placed in series in a circuit, their contributions to the total circuit
impedance are opposite. Capacitive reactance and inductive reactance
contribute to the total reactance as follows.
where: is the inductive reactance, measured in
ohms; is the capacitive reactance, measured in
ohms; is the angular frequency, times the
frequency in Hz. Although and are both positive by
definition, the capacitive reactance makes a negative contribution to total
reactance. Hence:
if , the total reactance is said to be inductive;
if , then the impedance is purely resistive;
if , the total reactance is said to be capacitive.
= Phase relationship = The phase of the voltage across a purely
reactive device lags the current by radians for a capacitive reactance and
leads the current by radians for an inductive reactance. Without knowledge
of both the resistance and reactance the relationship between voltage and current
cannot be determined. The origin of the different signs for
capacitive and inductive reactance is the phase factor in the impedance.
For a reactive component the sinusoidal voltage across the component is in
quadrature 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.
References Shamieh C. and McComb G., Electronics
for Dummies, John Wiley & Sons, 2011. Meade R., Foundations of Electronics,
Cengage Learning, 2002. 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.. Küpfmüller K. Einführung in die
theoretische Elektrotechnik, Springer-Verlag, 1959.
Young, Hugh D.; Roger A. Freedman; A. Lewis Ford [1949]. Sears and Zemansky's
University Physics. San Francisco: Addison Wesley. ISBN 0-8053-9179-7.
^ Irwin, D.. Basic Engineering Circuit Analysis, page 274. New York: John Wiley
& Sons, Inc. hyperphysics.phy-astr.gsu.eduhframe.html
See also Bioelectrical impedance analysis
Electrical measurements Susceptance
Magnetic reactance External links
Interactive Java Tutorial on Inductive Reactance National High Magnetic Field
Laboratory Reactance calculator