# EE115, Reactive inductance

Explain briefly why XL limits the amount of alternating current

Explain why XL increases with higher frequencies and more inductance. How might you use this fact in an application

Answers

The inductive reactance or in other words XL is by DEFINITION XL=omega*L where omega is the angular frequency of the current and L is the inductance. To get a short grasp of why XL it is opposing to the current flow through an inductor remember the Faraday law of the induced voltage in an inductor

$V = -L*d I/d t$

which means that every time a current flowing into an inductor changes value there is an opposite voltage on the inductor that forms.

In other words, if you have a variable (let say AC) voltage on the inductor, it causes a variable current through the inductor. This variation of this current will induce a voltage opposite to the initial voltage that caused the initial current flow, hence the current will DECREASE.

From the above relation one can see that this opposing tendency to the current flow is proportional to value of the inductance L and to the speed of the current changing (therefore the higher the frequency the higher the speed of variation and the higher the opposing induced voltage).

Since a reactance is a measure of the opposition to the current flow from the above observations it NEEDS to be

1. proportional to the inductance L

2. Proportional to the speed of current variation (or equivalent to the frequency, or angular frequency) $\omega=2*\pi*F$

$XL= \omega*L$

In practice there are numerous applications of this effect. On application will be to cancel the alternating component of a DC+AC signal one places in series inductances having enough XL values to reduce significantly the AC component of the signal. It is used in smoothing of the rectified AC voltages as well as in high or low frequency filters.

The observation that XL increases with frequency is used in tuned circuits (radios and TV) where with only a few windings one can attain the desired XL value since the frequency is high enough.

The same effect is used in High Frequency switching power supplies (see your computer), where instead of using high inductance and a large number of windings for the industrial frequency of 60 HZ, one makes an oscillating circuit on a very high frequency (100 kHZ), then rectifies this voltage with a diode and smooths the voltage with only small coils (low number of windings because the AC component of the rectified voltage has high frequency).