Editing Electrical reactance (section)

== Capacitive reactance ==

{{main|Capacitance}}
A capacitor consists of two [[Electric conduction|conductor]]s separated by an [[Electrical insulation|insulator]], also known as a [[dielectric]].

''Capacitive reactance'' is an opposition to the change of voltage across an element. Capacitive reactance <math>X_C</math> is [[inversely proportional]] to the signal [[frequency]] <math>f</math> (or [[angular frequency]] <math>\omega</math>) and the [[capacitance]] <math>C</math>.<ref name="Irwin">Irwin, D. (2002). ''Basic Engineering Circuit Analysis'', page 274. New York: John Wiley & Sons, Inc.</ref>

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 the negative number,<ref name="Irwin"/><ref>Hayt, W.H., Kimmerly J.E. (2007). ''Engineering Circuit Analysis'', 7th ed., McGraw-Hill, p. 388</ref><ref name="Glisson">Glisson, T.H. (2011). ''Introduction to Circuit Analysis and Design'', Springer, p. 408</ref>

:<math>X_C = -\frac {1} {\omega C} = -\frac {1} {2\pi f C}</math>.

Another choice is to define capacitive reactance as a positive number,<ref>Horowitz P., Hill W. (2015). ''[[The Art of Electronics]]'', 3rd ed., p. 42</ref><ref name="Hughes">Hughes E., Hiley J., Brown K., Smith I.McK., (2012). ''Hughes Electrical and Electronic Technology'', 11th edition, Pearson, pp. 237-241</ref><ref>Robbins, A.H., Miller W. (2012). ''Circuit Analysis: Theory and Practice'', 5th ed., Cengage Learning, pp. 554-558</ref>

:<math>X_C = \frac {1} {\omega C} = \frac {1} {2\pi f C}</math>.

In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. <math>Z_c=-jX_c</math>.

At <math>f=0</math>, the magnitude of the capacitor's reactance is infinite, behaving like an [[wikt:open circuit|open circuit]] (preventing any [[Electric current|current]] from flowing through the dielectric). As frequency increases, the magnitude of reactance decreases, allowing more current to flow.  As <math>f</math> approaches <math>\infty</math>, the capacitor's reactance approaches <math>0</math>, behaving like a [[short circuit]].

The application of a [[Direct current|DC]] voltage across a capacitor causes positive [[Electrical charge|charge]] to accumulate on one side and negative [[Electrical charge|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.