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Resistance, Reactance, and Impedance

Resistance, Reactance, and Impedance

I was tempted to call this subject "the three Rs of electrical theory", because it's one of the most standard subjects that every student probably learns in their first EE class; However, as you may have noticed, "Impedance" doesn't start with a letter R, so I couldn't do that. :( Nonetheless, these three forces, which are closely linked, are indeed important to the beginning electricity/electronics student. The good news is that they are relatively simple to understand, and can be dealt with using a few fairly easy and standard math formulas.

Resistance is a force that tends to resist the flow of electrical current. Resistance is usually created deliberately by a resistor, a device used to create resistance in a circuit. Resistance is pretty straightforward: The more resistive a resistor is (i.e. the more ohms it's rated for), the more it restricts the flow of electricity through it. Perhaps the best news of all is that if you're working with DC (Direct Current), resistance is the only thing you need to concern yourself with; the slightly more complicated concepts of reactance and impedance only exist in the world of AC (alternating current).

Reactance, unlike resistance, is usually undesirable in a circuit. Whereas resistance is created by a resistor to achieve some effect, reactance is an unfortunate by-product of certain electrical components. There are two basic types of reactance: Capacitive reactance and inductive reactance. Appropriately enough, capacitive reactance is created by capacitors, while inductive reactance is created by inductors. Using either of these device types in an AC circuit will introduce some reactance. Like resistance, reactance is expressed in ohms, and it behaves in much the same way as resistance, in the sense that it tends to restrict the flow of current through a circuit.

The formula for calculating inductive reactance is as follows:

XL = 2*pi*f*L

XL is the inductive reactance. X is the general electrical symbol for "reactance", and L is the symbol for "inductance" or "inductor", so put them together and you get the reactance of an inductor.

pi is, as you probably guessed, the famous ratio of a circle's circumference to its diameter, to wit: 3.14, etc.

f is the frequency of the AC flowing through the circuit.

L is the inductance of the inductor, in henries.

So you see, when you muliply 2 by pi, by the frequency of the AC, by the inductance of the inductor, the resultant value is the inductive reactance of the circuit.

The formula for capacitive reactance is similar, but there's a twist to it:

        1
XC = --------
     2*pi*f*C

XC is, as you might have guessed, the capacitive reactance, and C is the capacitance of the capacitor (in farads).

The two formulas for inductive reactance and capacitive reactance create interesting counterpoints. Notice that for inductive reactance, as the frequency of the AC increases, so does the reactance. Higher frequencies result in lower current. The opposite is true of capacitive reactance: The higher the frequency of AC, the less reactance a capacitor will present.

Similarly, a more inductive inductor will present more reactance, while a capacitor with more capacitance will yield less reactance.

Once you know the resistance and reactance of a circuit, the impedance is actually the overall opposition to current presented by the circuit. The impedance of a circuit is also expressed in ohms; Unfortunately, you cannot simply add the resistance and the reactance to get the impedance. The formula is a bit tricker than that, but for those who learned the Pythagorean Theorem, well, you'll finally have a place to use it here.

The total impedance of a circuit is the square root of the sum of the squares of the resistance and reactance. In other words, impedance can be represented as the hypotenuse of a right triangle. Resistance can be one of the shorter sides of the right triangle, and reactance can be the other shorter side. The longest side, the hypotenuse, is then the impedance. If you learned (and remember) the Pythagorean Theorem, you know that the square of the longest side of a right triangle is equal to the added squares of the other two sides. This formula is sometimes expressed as a squared + b squared = c squared, with a and b being the shorter sides of the triangle, and c being the longest side. Impedance, then, is:

Z = sqrt( (R^2) + (X^2) )

That is, impedance (which has a standard electrical symbol of Z, for some warped reason) is the square root of (resistance squared plus reactance squared).

And, well, there you go. That's resistance, reactance, and impedance. Now you should be able to pass Electricity 101. Party on.

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