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# Inductive Reactance Formula

Electricity is ubiquitous in the modern world. From the point of view of exams also it is an important topic as many questions come from that topic. Let us learn about the topic of Inductive reactance and the Inductive Reactance Formula.

## What is Inductive Reactance?

An inductor is a coil of wire. An electrical field is generated when a current passes through the coil i.e. the inductor. Thus an electric field has been “induced”. The induced field is directly proportional to the length of the coil or the number of turns in the coil. This is called “inductance.” In inductors, the current lags the voltage by 90 degrees.

When a voltage is applied across the terminals of an inductor it generates energy. This energy is stored in the form of a magnetic field. Inductors own self-induced or back emf value determines the growth of the current flowing through it and is not instant.

The resistance to the flowing current offered by an inductor in an AC circuit is known as impedance. In DC circuit it is known as reactance. Complex numbers are used to denote these quantities when analysing such circuits. Phase diagrams of such quantities can be drawn to understand them better. These quantities are used extensively in complex analysis.

### The Formula:

Inductive reactance or simply reactance is the resistance of an inductive circuit. It is termed as reactance because it is slightly different from the resistance offered by any device. And it is denoted as XL.

Inductive reactance is the resistance offered by the inductive circuit. It is the opposition to a changing current flow offered by an inductor. The SI unit for it is Ohm(Ω). The inductive reactance formula is:

Inductive reactance(XL) : 2π f L

where f is the frequency of the alternating current measured in Hertz(hz) and L is the inductance measured in henry(h).

It is proportional to the frequency of the current and hence inversely proportional to the Time.

XL α f and XL α (1/T).

Indicators like inductive reactances are used for designing inductors and also while designing circuits, power stations, transformers etc. Since inductors are an important component of designing it is important to know its inductive reactance. Thus it becomes mandatory for suppliers to specify the inductive reactances of the inductors while manufacturing them as those numbers play a very important role in deciding where a particular inductor will be used.

Studying the inductive reactance is important as many complex problems asked in competitive exams have sub-problems wherein calculation of inductive reactance is asked.

## Solved Examples for Inductive Reactance Formula

Q: An inductor of 2H is connected to a circuit at a frequency of 50Hz. Find out the inductive reactance of this circuit using inductive reactance formula

f = 50Hz and L = 2H

Inductive reactance formula is given as,

XL  = 2πfL

XL  = 2×3.14×50×2 = 628Ω.

Q: At what frequency does a 2500mH inductor have 6kΩ of reactance?

XL = 6kΩ = 6000Ω,  and

L = 2500mH = 2.5H

Inductive reactance formula is articulated as,

XL  = 2π fL

$\dpi{120}&space;\large&space;So,&space;f=&space;\frac{X_{L}}{2\pi&space;L}$

f = 6000 * 7/ (2 * 22 * 2.5) = 381.82 Hz.

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