Capacitive Reactance Formula

Capacitive Reactance Formula

In the RC Network, we know that when a DC voltage is supplied to a capacitor, it pulls a charging current from the power source. It also charges up to the voltage that is applied. Similarly, when the supply voltage decreases, the charge stored in the capacitor decreases, and it discharges. As the capacitor charges or discharges, current passes through it. This current is controlled by the capacitor’s intrinsic impedance. This internal impedance is commonly known as capacitive reactance. In this post, we’ll look at the capacitive reactance formula and ideas using an example. Let’s learn about a fascinating topic!

What is Capacitive Reactance?

Capacitive reactance, denoted as XC, is a measure of a capacitor’s resistance to an alternating current. It is measured using the same unit as resistance: ohms. However, reactance is inherently more complicated than resistance. This is because its value is proportional to the frequency f of the electrical signal that passes through the capacitor.

We know that a capacitor stores current. In electrical systems, reactance refers to the opposition of a circuit element to changes in current or voltage. When the capacitor is linked to a direct current supply, it charges to the specified voltage. It functions as a temporary storage device, maintaining the charge as long as the supply voltage is present.

Resistance has a set value, such as 100 Ω or 10,000 Ω. Capacitive reactance, on the other hand, fluctuates with applied frequency, therefore any change in supply frequency has a significant impact on the capacitive reactance value.

As the frequency rises, the capacitor will transmit more charge across the plates in a given period. As a result, more current flows through the capacitor, making it appear that the capacitor’s internal impedance has reduced. Thus, a capacitor linked to a circuit that varies over a specific frequency range can be described as Frequency Dependant.

The Formula for Capacitive Reactance

It is computed with the following formula:

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

Where,

Solved Examples on Capacitive Reactance

Example 1: Find the capacitive reactance value of a 120 nF, capacitor at a frequency of 10 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 = 10 kHz = 10000 Hz

C = 120 nF = 120 ×10^(-9) F

Thus applying the formula:

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

$$X_C =\frac{1}{2 \times\;3.14 \times 10000 \times 120 \times 10^{-9} }$$

$$X_C =0.0007238 \times10^{6}$$