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# Inductive Reactance Help

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By — McGraw-Hill Professional
Updated on Sep 9, 2011

## Introduction

In dc circuits, resistance is a simple thing. It can be expressed as a number ranging from zero (a perfect conductor) to extremely large values, increasing without limit through thousands, millions, and billions of ohms. Physicists call resistance a scalar quantity because it can be expressed on a one-dimensional scale. In fact, dc resistance can be represented along a half-line (also called a ray ).

Given a certain dc voltage, the current decreases as the resistance increases in accordance with Ohm’s law. The same law holds for ac through a resistance if the ac voltage and current are both specified as peak, pk-pk, or rms values.

## Inductors And Dc

Suppose that you have some wire that conducts electricity very well. If you wind a length of the wire into a coil and connect it to a source of dc, the wire draws a small amount of current at first, but the current quickly becomes large, possibly blowing a fuse or overstressing a battery. It does not matter whether the wire is a single-turn loop, lying haphazardly on the floor, or wrapped around a stick. The current is large. In amperes, it is equal to I = E/R , where I is the current, E is the dc voltage, and R is the resistance of the wire (a low resistance).

You can make an electromagnet by passing dc through a coil wound around an iron rod. However, there is still a large, constant current in the coil. In a practical electromagnet, the coil heats up as energy is dissipated in the resistance of the wire; not all the electrical energy goes into the magnetic field. If the voltage of the battery or power supply is increased, the wire in the coil, iron core or not, gets hotter. Ultimately, if the supply can deliver the necessary current, the wire will melt.

## Inductors And AC

Suppose that you change the voltage source connected across a coil from dc to ac. Imagine that you can vary the frequency of the ac from a few hertz to hundreds of hertz, then kilohertz, and then megahertz.

At first, the ac will be high, just as is the case with dc. However, the coil has a certain amount of inductance, and it takes a little time for current to establish itself in the coil. Depending on how many turns there are and on whether the core is air or a ferromagnetic material, you’ll reach a point, as the ac frequency increases, when the coil starts to get sluggish. That is, the current won’t have time to get established in the coil before the polarity reverses. At high ac frequencies, the current through the coil has difficulty following the voltage placed across the coil. Just as the coil starts to “think” that it’s making a good short circuit, the ac voltage wave passes its peak, goes back to zero, and then tries to pull the electrons the other way. This sluggishness in a coil for ac is, in effect, similar to dc resistance. As the frequency is raised, the effect gets more pronounced. Eventually, if you keep on increasing the frequency of the ac source, the coil does not even come near establishing a current with each cycle. It then acts like a large resistance. Hardly any ac current flows through it.

The opposition that the coil offers to ac is called inductive reactance . It, like resistance, is measured in ohms (Ω). It can vary just as resistance does, from near zero (a short piece of wire) to a few ohms (a small coil) to kilohms or megohms (bigger and bigger coils or coils with ferromagnetic cores at high frequencies). Inductive reactance can be depicted on a ray, just like resistance, as shown in Fig. 15-3.

Fig. 15-3 . Inductive reactance can be represented on half-line or ray. There is no limit to how large it can get, but it can never be negative.

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