# Reactance

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 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 reciprocal of reactance is susceptance.

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

[itex]Z = R + j X \,[itex]

where

Z is impedance, measured in ohms

R is resistance, measured in ohms

X is reactance, measured in ohms

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

[itex]\left | Z \right | = \sqrt {R^2 + X^2} \,[itex]

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

Inductive reactance (symbol XL) 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 with the frequency (hence zero for DC). There is also a phase difference between the current and the applied voltage.

Inductive reactance has the formula

[itex]X_L=2\pi fL \,\![itex]

where

XL is the inductive reactance, measured in ohms

f is the frequency, measured in hertz

L is the inductance, measured in henry

Capacitive reactance (symbol XC) reflects the fact that electrons can not 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

[itex]X_C= \frac {1} {2\pi fC} \,[itex]

where

XC is the capacitive reactance measured in ohms

f is the frequency, measured in hertz

C is the capacitance, measured in farad

## SI electricity units

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