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Conductance, Susceptance, and Admittance

Conductance, Susceptance, and Admittance

If you studied Resistance, Reactance, and Impedance, then you have a pretty good start in the basics of opposition to electric current. However, these three forces each have a twin, which is essentially their opposite. While resistance, reactance, and impedance all tend to restrict how much electricity can flow through a certain path, conductance, susceptance, and admittance are all forces that tend to allow electricity to flow. And there's good news: All of these forces are quite easy to understand and mathematically calculate.

Conductance is the opposite of resistance. While resistance is the restriction of current because of the chemical composition of a substance, conductance is the ability to conduct electricity of a certain material. Conductance is measured in siemens (S). Conductance is the reciprocal of resistance; That is to say, conductance is 1 divided by resistance. For example, if you have a 1,000 ohm resistor, its conductance is 1 divided by 1000, or 0.001 siemens. (This would probably be expressed by an engineer as 1 mS, one millisiemen.) The conductance of a 470 ohm resistor is about 2.13 mS. Notice that as resistance goes down, conductance goes up. Conductance's electrical symbol is G.

Susceptance (symbolized with a B) is the opposite of reactance. Just as there's capacitive reactance and inductive reactance, so too there is capacitive susceptance (BC) and inductive susceptance (BL). Just like with conductance, both of these are the reciprocal of their corresponding reactances. That is to say, capacitive susceptance is 1 divided by the capacitive reactance, and inductive susceptance is 1 divided by the inductive reactance. There's an added little nuance that should be noted to make these calculations easier, though. Recall that capacitive reactance is calculated as follows:

   1
--------
2*pi*f*C

To get the capacitive susceptance, you would divide that by 1, meaning there would be an additional line on top, with another 1 above that, like this:

   1
--------
   1
--------
2*pi*f*C

...But all this is not necessary, because the two divide-one-by operations cancel each other out. Thus, capacitive susceptance can be simplified into the following equation:

BC = 2*pi*f*C

Inductive susceptance, meanwhile, becomes exactly like the formula for capacitive reactance, except that it of course uses inductance rather than capacitance:

        1
BL = --------
     2*pi*f*L

Susceptance is measured in siemens, too.

And finally, we come to admittance, symbolized by the letter Y, which is the opposite of impedance. You'll be glad to know (perhaps) that the formula for calculating admittance is identical to that of impedance, except that you use conductance and susceptance to calculate admittance (not resistance and reactance, as you do with impedance). So...

Y = sqrt( (G^2) + (B^2) )

If you can calculate impedance, admittance should give you no problem. Admittance is even measured in siemens, so this is all consistent across the board.

Conductance, susceptance, and admittance are sometimes called the "evil twins" of resistance, reactance, and impedance, but in fact they are not so bad; As you've seen, they are certainly not calculated too much differently from their opposite counterparts, and once you understand these concepts, you should be pretty well set for a college degree in electronics. And remember: Yes, you can use a calculator.

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