Inductive Reactance of 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:
\(\pi\) is here a mathematical constant with the value \( \pi = 3.14 \). The unit of the inductive reactance is Ohm:
By the way, the factor \( 2 \, \pi \, f \) in Eq. 1
is often combined to angular frequency \( \omega \):
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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.
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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.
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
:
&~=~ 157 \, \mathrm{\Omega}
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 \(X_{\text L}\):
Insert the \(230 \, \mathrm{V} \) RMS voltage and \( 157 \, \mathrm{\Omega} \), then you get the RMS current:
&~=~ 1.5 \, \mathrm{A}