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Capacitive Reactance Formula

Capacitive reactance ( XC) is a measure of a capacitor’s opposition to alternating current. It is measured in ohms like resistance but reactance is more complex than resistance because its value depends on frequency (f) of the electrical signal passing through the capacitor

A Capacitor is a current storing device. In electrical and electronic systems, reactance is all about the opposition of a circuit element to changes in current or voltage due to that element’s capacitance. 

When the capacitor is connected to a DC supply voltage, it becomes charged to the value of the applied voltage, acts as a temporary storage device and maintains this charge as long as the supply voltage is present.

Capacitive Reactance Formula is expressed by

Where in,

L = inductance of the circuit,

C = capacitance and

f = frequency of ac mains

Example 1

Calculate the capacitive reactance if 40 mF is connected to a frequency generator of 50 Hz signal. 

Solution

According to given parameters

F= 30 x 10-3

C = 50Hz

 The capacitance reactance formula is given by

Xc = 1 / 2πfC

    = 1 / 2π×40×10−3×50

    = 0.106 Ω 

Example

Calculate the reactance of capacitance in an AC circuit wherein the input signal has a frequency of 100 Hz and a capacitor has a capacitance of 1000mF in a circuit.

Solution 

Given

 Frequency f is 100 Hz

Capacitance C is 1000 mF 

The capacitance reactance formula is given by 

xc = 1 / 2πfc 

xc = 1 / 2 π x 200 x 1000 x 10-3 

    = 7.961 Ω   

Hence, the capacitive reactance is 7.961 Ω