# Electrical reactance

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. 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 ${\displaystyle \scriptstyle {X}}$. 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 also goes up and capacitive reactance goes down.

## Capacitive reactance

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

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

There are two choices in the literature for defining reactance for a capacitor. One is to use a uniform notion of reactance as the imaginary part of impedance, in which case the reactance of a capacitor is a negative number:[1][2][3]

${\displaystyle X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}}$

Another choice is to define capacitive reactance as a positive number,[4][5][6]

${\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}$

In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. ${\displaystyle Z_{c}=-jX_{c}}$.

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 (ideal AC current source), a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge is returned to the source. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.

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