Capacitive Reactance

Capacitive reactance, abbreviated as \(X_c\), is the opposition to holding an electric charge.  It is used in electrical engineering and physics, particularly in the study of alternating current circuits.  It refers to the opposition or resistance that a capacitor presents to the flow of alternating current, just like resistance opposes the flow of direct current.

When an AC voltage is applied to a capacitor, the capacitor charges and discharges in response to changes in the voltage.  This charging and discharging behavior creates an opposition to the flow of current, which is known as capacitive reactance.  As the frequency of the AC signal increases, the capacitive reactance decreases, and vice versa.  This means that capacitors allow more current to flow at higher frequencies and less current at lower frequencies.  This property is utilized in various electrical and electronic circuits for purposes such as filtering, coupling, and energy storage.

Key Points about Capacitive Reactance

Inversely Proportional to Frequency  -  Capacitive reactance is inversely proportional to the frequency of the AC signal.  As the frequency increases, the capacitive reactance decreases, and vice versa.
Impedance in AC Circuits  -  Impedance is a measure of the total opposition that a circuit presents to the flow of AC.
Phasor Representation  -  Like resistance in DC circuits, capacitive reactance can be represented as a phasor in the complex plane.  The angle of the phasor is determined by the phase relationship between the voltage across the capacitor and the current flowing through it.
Units  -  Capacitive reactance is measured in ohms, the same unit as resistance.
Role in Filtering  -  Capacitors and their associated capacitive reactance play a crucial role in filtering applications in electronics.

Remember that capacitive reactance is associated with capacitors in AC circuits, and it is part of the broader concept of impedance in AC circuit analysis.

 

Capacitive Reactance formula
\( X_c \;=\;   1 \;/\; 2 \; \pi \; f \; C \)     (Capacitive Reactance) \( f \;=\;   1 \;/\; 2 \; \pi \;  X_c \; C \) \( C \;=\;   1 \;/\; 2 \; \pi \; f \; X_c \)
Symbol	English	Metric
\( X_c \) = Capacitive Reactance	-	\(kg-m^2\;/\;s^3-A^2\)
\( \pi \) = Pi	-	\(3.141 592 653 ...\)
\( f \) = Frequency	-	\(s^{-1}\)
\( C \) = Capacitance	-	\(s^4-A^2\;/\;kg-m^2\)