Impedance of Inductor formula (Inductive reactance)

In another article, we have discussed the electrical impedance of various circuit components like resistors, capacitors, inductors and their combination (LC, RLC, RC circuits). In this communication, we are going to be more specific. Here, we are to discuss the electrical impedance of an inductor coil and all related facts. Also, we will learn to calculate the impedance of inductors by solving numerical problems on it.

First we have to know What is inductor? The inductor is a circuit component just like a resistor, capacitor, etc. The symbol of the inductor is L. More precisely, the effect of the inductor is the inductance which has the symbol as L. An inductor also offers opposition to the change in current through it. This opposition is known as the impedance of inductive coil.

Other names of the Impedance of inductor:

  1. Inductance
  2. Inductive reactance
  3. Resistance of inductor

What is the impedance of an inductor?

Electrical impedance of an inductor gives the measurement of the opposition to the change in electric current through the inductor coil. The most common name of impedance of inductors is the inductive reactance. Conceptually, electrical inductance is very much similar to the electric resistance. Sometimes, inductance is called the resistance of inductor. But there are some differences in nature and uses.

The unit of the inductance is Henry (H), but the unit of the impedance is Ohm.

Equation for inductor reactance in a coil

If an alternating voltage of angular frequency \small \mathbf{\omega } is applied across an inductor of inductance L, then the reactance or the impedance offered by the inductor to the alternating current through it is, \small {\color{Blue} Z_{L}= j\omega L}………(1)

Here, j is the imaginary unit (\small j=\sqrt{-1}).

And, the magnitude of the impedance of the inductor is, \small {\color{Blue} Z_{L}= \omega L}………..(2)

This is the formula of inductive reactance or inductive impedance of a coil. Sometimes, it is called the inductor equation.

What is the impedance offered by inductor to the flow of DC?

In the equation of inductive reactance or impedance one can see that the impedance is directly proportional to the angular frequency of the current flow through the coil. Now, a direct current (DC) has zero angular frequency.

Inductors will offer an opposition to a change in current flow. But, the direct current never changes its magnitude and direction. Therefore, the inductor will not offer any impedance to the DC.

How do you calculate the impedance of inductors?

Now, we are to calculate inductance and inductive reactance by using the inductor equation \small {\color{Blue} Z_{L}= \omega L}.

1. An 3 mH inductor coil is operating on 50 Hz alternating current. Find the inductive impedance of the coil.

Answer: Inductance of the inductor, L = 3 mH = 3×10-3 Hz, Linear frequency, f = 50 Hz. Then angular frequency, \small \omega = 2\pi f = 314 rad/s.

Thus, the impedance of the inductor is, ZL = wL = 314×3×10-3 ohm = 0.942 Ohm

2. Find the impedance of 25 mH inductor at 50 Hz.

Answer: Here, the frequency is f = 50 Hz. Then angular frequency, w = 314 rad/s (similar to above problem)

Inductance of the inductor, L = 25 mH = 25×10-3 H,

Therefore, the impedance or the inductive reactance is, ZL = wL = 314×25×10-3 = 7.85 Ohm

This is all from this article. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

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  1. Electrical impedance

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