Inductive Reactance of a Coil

Video: Inductive reactance of a coil briefly explained

AC voltage source applied to a coil
A time-dependent alternating voltage is applied to a coil.

If we apply an AC voltage \( U_{\text L}(t) \) to a coil of inductance \( L \) , then an AC current \( I_{\text L}(t) \) flows through the coil. The alternating voltage changes polarity with the frequency \(f\). With this frequency, the alternating current also changes its direction.

A coil to which an alternating voltage is applied has a complex non-ohmic resistance which is called inductive reactance. This resistance is usually abbreviated as \( X_{\text L} \).

You can easily calculate the inductive reactance. You need the AC frequency \( f \) and the inductance \( L \) of the coil:

Formula anchor

\(\pi\) is here a mathematical constant with the value \( \pi = 3.14 \). The unit of the inductive reactance is Ohm:

Unit of inductive reactance
Formula anchor

By the way, the factor \( 2 \, \pi \, f \) in Eq. 1 is often combined to angular frequency \( \omega \):

Formula: Inductive reactance using angular frequency
Formula anchor
  • If you use a very large AC frequency, then the inductive reactance will also be very large and the coil will barely let the current through.

  • If, on the other hand, the AC voltage frequency is very small or even zero, that is if a DC voltage is applied, then the inductive reactance also becomes zero. The coil allows an arbitrarily high current to pass, which corresponds to a short circuit.

As you can see from Eq. 1 or 2, you can also use the inductance \( L \) to adjust the reactance of the coil.

Example: Calculate reactance of coil

You apply \( 230 \, \mathrm{V} \) to a coil with an inductance of \( 500 \, \mathrm{mH} \) (Millihenry). The applied rms voltage has a frequency of \( 50 \, \mathrm{Hz} \). Insert inductance and frequency into Eq. 1:

Example calculation: Inductive reactance
Formula anchor

To determine the RMS current \(I_{\text{eff}}\) flowing through the coil, use the URI formula. Instead of using the ohmic resistance \(R\), use the inductive reactance \(X_{\text L}\):

Formula: RMS current using coil reactive resistance
Formula anchor

Insert the \(230 \, \mathrm{V} \) RMS voltage and \( 157 \, \mathrm{\Omega} \), then you get the RMS current:

Example calculation: Determine RMS current using coil resistance
Formula anchor

+ Perfect for high school and undergraduate physics students
+ Contains over 500 illustrated formulas on just 140 pages
+ Contains tables with examples and measured constants
+ Easy for everyone because without vectors and integrals

Learn more