What is an Inductive Reactance : Definition, Unit and Formula

One of the famous laws related to electricity is “Ohm’s Law”.  Ohms law gives an empirical relation that describes the conductivity of various electrically conductive materials. According to this law, the current flowing in a conductor is directly proportional to the voltage across the conductor, with resistance as a proportionality constant. Here, the units of current are  Ampere, units of voltage are given in volts, and units of resistance are Ohms. In physics, this law is usually also used to refer to various generalizations of the law, such as in Vector form in electromagnetics. Similarly, when working with AC inductors, ohms law is used, where resistance is referred to as “Inductive Reactance” instead of “resistance”.

What is Inductive Reactance?

When voltage is applied to an inductor, a current is induced across the inductor circuit. However, this current is not generated instantly but grows at a rapid rate determined by the inductor’s self-induced values. The induced current is limited by the resistive elements present in the inductor coil windings. Here, the amount of resistance depends on the ratio of the applied voltage to the induced current, as mentioned in Ohm’s Law.

The figure below is an Inductor circuit used to calculate the inductive reactance.

However, when the inductor is connected to the AC circuit the flow of current behaves differently. Here, the sinusoidal supply is used. Hence, a phase difference between voltage and current waveform occurs. Now, when AC supply is used for the inductor coil, besides the inductance of the coil the current also has to face opposition from the frequency of the AC waveform. This resistance faced by the current in inductor while connected in AC circuit is named as “Inductive Resistance”.

Difference Between Inductance and Reactance

Inductance is the capability of a material to induce a voltage in it when there is a change in the current flow within it. The symbol for inductance is “L”. Whereas, reactance is the property of electrical materials that opposes the change in current. The units of reactance are “Ohm’s” and it is denoted by the symbol “X” to distinguish it from normal resistance.

Reactance works similarly to electrical resistance but unlike resistance, reactance does not dissipate power as heat. Rather it stores the energy as a reactance value and returns it to the circuit. An ideal inductor has zero resistance whereas an ideal resistor has zero reactance.

Inductive Reactance Formula Derivation

Inductive reactance is the term related to AC circuits. It opposes the flow of current in AC circuits. In an AC inductive circuit due to phase difference, the current waveform “LAGS” the applied voltage waveform by 90 degrees .i.e if the voltage waveform is at 0 degrees, the current waveform will be at -90 degrees.

In an Inductive circuit, the inductor is placed across the AC voltage supply. The self-induced emf in the inductor increases and decreases with the increase and decrease in the supply voltage’s frequency. Self-induced emf is directly proportional to the rate of change of current in the inductor coil. The highest rate of change occurs when the supply voltage waveform crosses over from the positive half cycle to a negative half cycle or vice-verse.

In an inductive circuit, the current lags the voltage. So, if the voltage is at 0 degrees then the current will be at -90 degrees with respect to voltage. Hence, when sinusoidal waveforms are considered, voltage waveform V_L  can be classed as a sine wave and current waveform I_L as a negative cosine wave.

Thus, current at a point can be defined as:

I _L = I_max. sin(ωt – 90 ⁰) , φωis in radians and ‘t’ in seconds

The ratio of voltage and current in the inductive circuit gives the value of inductive reactance X_L

Thus , X_L  = V_L / I_L ohms = ωL = 2πfL ohms

Here, L is the inductance, f is the frequency, and 2πf  = ω

From this derivation, it can be seen that the Inductive reactance is directly proportional to frequency ‘f’ and inductance ‘L’ of the inductor. With an increase in either frequency of voltage or inductance of the coil, the overall reactance of the circuit increases. As the frequency increases to infinity, the inductive reactance also increases to infinity acting similar to an open circuit. For a dip in frequency to zero, the inductive reactance also decreases to zero, acting similar to a short circuit.

Symbol

Inductive reactance is the resistance faced by the current flow in the inductor when AC voltage is supplied. Its units are similar to units of resistance. The symbol of inductive reactance is “X_L“. As the current lags by 90 degrees with respect to voltage inductor, by having the value for either of the quantity the other can be calculated easily. If the voltage is known, then by the negative 90-degree shift of voltage waveform the current waveform can be derived.

Example

Let’s look at an example to calculate the inductive reactance.

An inductor with inductance 200mH and zero resistance is connected across a 150v voltage supply. The frequency of voltage supply is 60Hz. Calculate the inductive reactance and the current flowing through the inductor

Inductive Reactance

X_L  = 2πfL

= 2π × 50 × 0.20

= 76.08 ohms

Current 

I_L = V_L / X_L

= 150/76.08

= 1.97 A

In electrical and electronic circuits the term ‘reactance’ is regularly used with inductor and capacitor circuits. An increase in the reactance value in these circuits leads to a decrease in current across them. Inductive reactance causes voltage and current to go out-of-phase. In electrical power systems, this will limit the power capacity of AC transmission lines. Although current still flows in such situations but transmission lines will get heated up and there will be no effective power transfer. So, it is important to monitor the inductive reactance of the circuits. What is the phase difference between voltage and current waveforms for the inductor circuit?