Inductor mathematics (AC)

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How the inductor works

Inductor family

Inductor color code

Series and parallel circuits

Calculating time constant

Making Circuit boards

Introduction

Although the equation on the last page is great for calculating the time it would take to charge and discharge an inductor in a circuit with DC power, it is impractical for AC circuits.

Psychology if the Inductor

In an AC circuit, the inductor acts more like a resistor then any other component because it resists any kind of current change whether it is positive or negative current flow. So when power starts to charge to a peak voltage of lets say 10v and before the inductor can fully charge, the current changes direction. But the nature of the inductor is that the flux lines create a counter voltage until the flux lines can get established in a directional flow. When current changes direction within the inductor the flux lines are still rotating in one direction and it takes energy to make these flux lines change in the opposite direction. Because AC changes direction many tines a second "60 times from US wall sockets" the inductor doesn't fully establish its full direction and in affect is always generating a small amount of current in the opposite direction. This makes waveforms just a little flatter but is perfect in applications like power supplies and audio applications where you want to distort alternating DC "ripple" power or voice signals.

If you were to make an inductor perfectly designed with no resistance and have a source of infinite inductance then the outcome would be zero volts. This is because in AC power, voltage fluctuates from a positive voltage to an equal amount of negative voltage and the center point or average voltage is zero.

Applications

   Since AC current is always changing we will be using Pi in our equation to determine the affects on wavelengths.

   To determine the results if an inductor on a Alternating Current you will need to use a calculator and some known facts about your circuit and power input like the frequency of which the current changes (Hz) and the inductance values of your circuit. Now this is not an equation that can predict all points on an AC wave but calculates the maximum of positive and negative voltage levels.
   These most positive and negative points are known as Peak and Peak-to-Peak values. A peak value is one that can be positive or negative in nature but is referenced to GROUND, a voltage source that is nether positive or negative in nature.
   A Peak-to-Peak value rating is one that takes the most positive and most negative voltage values and adds then together to calculate the total current or voltage differences.

Do the math

Click here for notation table
Calculator

   Although in you circuit you will be measuring in ether peak or peak to peak values, it makes no difference in the equation you are about to learn.

XL=(2*P)FL

Where XL = inductive reactance

P = 3.1415
F = frequency (Hz)
L = inductance values (Henries)

   So lets say that we have an inductance of 250 mH and a frequency of 60Hz (US power from wall sockets) , to determine the inductive reactance lets follow the equation above.
(2P)*(Frequency)*(inductance)
6.28 * 60 * 250mH = 94200

   Since we are using the mili unit we need to convert back so that we can express our result in ohms. Since we have a unit of mili which is 0.001 and a total result of 94200 we now need to add the two together which would gives us a total of:
94.2 or 94.2 ohms.
   So in an AC circuit the inductor would introduce 94.2 ohms for every peak value or twice the amount for peak-to-peak values.

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