# Inductive Reactance and Capacitive Reactance

## What Is An Electrical Reactance?

An electrical reactance can be defined as a flow that is opposite in the direction of current in a circuit element because of its inductance and capacitance. If the reactance is greater, then the current will be smaller for the same applied voltage. Reactance being almost similar to electric resistance also differs from it in a few ways. When an alternating current is made to pass through the electric circuit or element, both the phase as well as the amplitude of current will change. Also, the energy is stored in the element containing reactance.

The energy is thus released either in the form of an electric field or magnetic field. The reactance in the magnetic field resists change in the current whereas, in the electric field, the reactance will resist the change in voltage. If the reactance releases energy in the form of a magnetic field, it is called inductive reactance whereas if the reactance releases energy in the form of an electric field, it is called capacitive reactance. With the increase in frequency, capacitive reactance is decreased, and inductive reactance is increased. An ideal resistor will have zero reactance, whereas ideal inductors and capacitors will have zero resistance.

### What is Inductive Reactance?

The inductive reactance is the reactance that is produced due to the inductive element (inductor). It can be denoted as XL . With the help of inductive elements, electrical energy can be stored in the form of a magnetic field. When an alternating current is passed through the circuit, the magnetic field is formed around it which can be changed as a result of the current. Changes in the magnetic field can induce another electric current in the same circuit. Lenz’s law states that the direction of this current is opposite to the main current. Therefore, we can say that the inductive reactance actually opposes the change of current through the element.

The current flow due to the inductive reactance results in the delay which may result in creating the phase difference between the current and the voltage waveforms. The current for the inductive circuit may lag the voltage. In an ideal inductive circuit, the current lags voltage by 90˚. The inductive reactance is also the reason why the power factor is lagging. The phasor diagram for the ideal inductive circuit is drawn below.

The Phasor Diagram of Ideal Inductive Circuit

### What is Capacitive Reactance?

The capacitive reactance can be defined as the reactance that is produced because of the capacitive elements (Capacitors). We can denote it as  XC. The capacitive reactance is an opposition of the voltage across the capacitive element which is temporarily used to store electrical energy in the form of an electric field. The capacitive reactance creates a phase difference between the current and the voltage.

In the capacitive circuit, voltage is lead by the current. For an ideal capacitive circuit, the voltage lead by the current is 90˚. Thanks to capacitive reactance, due to which the power factor of the system or circuit leads. The phasor diagram for the ideal capacitance circuit is drawn below.

Phasor Diagram of Ideal Capacitive Circuit

### Difference Between Reactance and Resistance

1. The reactance is an AC component of impedance while the resistance is a DC component of Resistance.

2. The value of reactance is always a complex number whereas the value of resistance has to be a real number.

3. In a purely inductive or capacitive circuit, the resistance will be zero and in a purely resistive circuit, the reactance will be zero.

4. Due to reactance, both amplitude, as well as the phase of current, will change. Due to resistance, the current and voltage will always remain in phase.

5. The value of reactance is dependent on the supply frequency whereas the value of resistance is not dependent on the supply frequency.

6. For a DC supply, the inductive reactance has to be zero and the capacitive reactance will be infinite. For DC supply, the resistance will remain the same.

7. Reactances are denoted as X (XL and XC). Resistance is denoted as R.

8. The power factor in reactance is leading or lagging due to the reactance element. In Resistance, the power is unity when the reactance is zero.

### Solved Examples

Example 1) Find out the capacitive reactance (Xc) for an AC source of 100V and 50 Hz by a capacitor of capacitance, c = 20 μF.

Solution 1) Finding out the capacitive reactance (Xc):

XC = $\frac{1}{wc}$ = $\frac{1}{2πfc}$ = $\frac{1}{2π×50×20×10^{-6}}$ = $\frac{10^6}{1000π}X_c$ = $\frac{10^3}{x}$

Example 2) A capacitor offers Resistance of 100Ω to an AC source of 100 V and 50 Hz. Find out the value of capacitance C =?

Solution 2)

XC = $\frac{1}{wc}$ ⇒ c = $\frac{1}{x_cw}$ = $\frac{1}{100×2π×50}$

XC = $\frac{10^{-4}}{π}$

Question 1) What is the unit and formula of Inductive Reactance?

Answer 1) The inductive reactance and the frequency are directly proportional to each other which means that if the frequency increases, the inductive reactance will also increase. Inductive reactance is depended on the supply frequency as well as the inductance of that element. The inductive reactance formula can be written as:

XL=2πfL

The unit used for reactance is OHM (Ω).

Question 2) What is the unit and formula of Capacitive Reactance?

Answer 2) Capacitive reactance is inversely proportional to the supply frequency as well as the capacitance of that element which means if we increase the supply frequency, the capacitance will decrease. The formula for capacitance is written as:

XC = 1/2πfC

The unit used for capacitive reactance is the same as the unit used for inductive reactance i.e., OHM(Ω).