Capacitive Reactance Formula

In the RC Network, we know that when a DC voltage is applied to a capacitor, the capacitor itself draws a charging current from the supply. Also, it charges up to a value equal to the applied voltage. Similarly, when the supply voltage has reduced the charge stored in the capacitor also reduces and hence it discharges. As the capacitor charges or discharges, the current flows through it. This current is restricted by the internal impedance of the capacitor. This internal impedance is popular as Capacitive Reactance. In this article, we will discuss the capacitive reactance formula and concepts with an example. Let us learn the interesting topic!

Capacitive Reactance Formula

What is Capacitive Reactance?

Capacitive reactance represented as \(X_C\) is a measure of a capacitor’s opposition to the alternating current. It is measured in the same unit as in resistance i.e. ohms. But reactance is more complex in nature than the resistance. This is because its value depends on the frequency f of the electrical signal passing through the capacitor.

We know that a Capacitor is a current storing device. In electrical systems, reactance is used for the opposition of a circuit element in changes in current or voltage. When the capacitor is connected to the supply of DC, it becomes charged to the value of the given voltage. It acts as a temporary storage device and maintains this charge as long as the supply voltage is present.

Resistance has some fixed value like 100 \(\Omega, 10k \Omega\). On the other hand, Capacitive Reactance varies with the applied frequency, and hence any variation in supply frequency will have a big effect on the capacitive reactance value.

As the frequency increases, the capacitor will pass more charge across the plates in a given time. Then it will result in a greater current flow through the capacitor appearing as if the internal impedance of the capacitor has decreased. Thus, a capacitor connected to a circuit that changes over a given range of frequencies can be said to be Frequency Dependant.

The Formula for Capacitive Reactance

It is calculated using the following formula given as:

\(X_C\) = \(\frac{1}{2 \pi\;f\;C} \)

Where,

\(X_C\)	Capacitive Reactance
f	Frequency
C	Capacitance
\(\pi\)	3.14

Solved Examples

Q.1: Calculate the capacitive reactance value of a 220 nF, capacitor at a frequency of 1 kHz and again at a frequency of 20 kHz.

Solution:  Here: ƒ is the frequency in Hertz and C is the capacitance in Farads.

At a frequency of 1 kHz: we have,

f = 1 kHz = 1000 Hz

C = 220 nF = 220 \(\times 10^{-9} F\)

Thus applying the formula:

\(X_C\) = \(\frac{1}{2 \pi\;f\;C} \)

\(X_C\) = \(\frac{1}{2 \times\;3.14 \times 1000 \times 220 \times 10^{-9} } \)

\(X_C\) = \(0.0007238 \times10^{6} \)

\(X_C\) = \(723.8 \Omega\)

Again at the frequency of 20 kHz: we have,

f = 20 kHz = 20000 Hz

C = 220 nF = 220 \(\times 10^{-9} F \)

Thus applying the formula:

\(X_C\) = \(\frac{1}{2 \pi\;f\;C} \)

\(X_C\) = \(\frac{1}{2 \times\;3.14 \times 20000 \times 220 \times 10^{-9} } \)

\(X_C\) = \(36.2  \Omega\)

Therefore, it is obvious from above that as the frequency applied across the 220 nF capacitor increases, from 1kHz to 20kHz. Then its reactance value, decreases, from 723.8 \(\Omega  to just 36.2 \Omega\).