Capacitive Reactance Formula

What is Capacitive Reactance?

Capacitive reactance defines the opposition presented to alternating current (AC) by a capacitor, due to its capacity to store and release electrical energy; it's not like resistance, which is lost as heat when it dissolves. Capacitive reactance makes capacitors influence the phase relationship between voltage and current in circuits. It is inversely proportional to both the frequency of the AC signal and the capacitance of the capacitor.

Capacitive reactance has numerous applications in filtering, timing circuits, and power factor improvement in AC systems, thus it is one of the most important concepts to understand the behavior of an AC circuit.

Formula 

The capacitive Reactance Formula is described by

  Where in,

• C = capacitance in farads 

•  f = frequency in hertz 

• Xc  =  the capacitance reactance measured in ohms 

Solved Problems 

Problem 1: Determine the capacitive reactance if 40 mF is connected to a frequency generator of 50 Hz signal. 

Solution: 

Given,  

C= 40 mF 

F = 50Hz 

The capacitance reactance formula is described as

 Xc = 1 / 2πfC 

      = 1 / 2×3.14× 40×10−3×50 

      = 0.07961Ω 

Problem 2: Determine the capacitance reactance in an AC circuit where the input frequency is 100 Hz and a capacitor is used having a capacitance of 1000 mF in a circuit.

Solution:

Given,

F = 100 Hz

C = 1000 mF

The capacitance reactance formula is given;

xc = 1 / 2πfc

xc = 1 / 2  x 3.14  x 100  x 1000  x 10-3

     = 1.5  x 10-3 Ω

Thus, the capacitive reactance is 1.5 x 10-3Ω