# Transformer - the inductive resistance

As I recently learned, the inductive resistance and capacitor resistance in a circuit are opposite and therefore need to be subtracted. And since transformers are basically big coils of wire, where I assume there's inductive resistance, shouldnt adding capacitors to the circuit lessen the overall resistance?

Or am I understanding this wrong?

fawk3s

I suspect that your have misunderstood something?

In ordinary circuit analysis your have resistance, capacitance and inductance. None of them can be used to cancel the other.

The effect on the phase relationship between voltage and current is opposite for a capacitance and an inductance.

But this does not mean that you can e.g. cancel the effect of an inductor by putting in a capacitor.

The only way to cancel the impedance introduced into the circuit by a resistor, inductor or capacitor is to bypass it.

According to the formula

Z = (sqrt) R^2 + (Xc-Xl)^2

where Z is the overall resistance or the impedance, R is the "wire resistance", and Xc and Xl are the resistances of the capacitor and inductor,
adding a certain capacitor to a certain inductor should lessen the overall resistance.
Say, Xc and Xl were equal. The only resistance in the circuit would be the actual wire resistance.
Or am I understanding the meaning of Z / the overall resistance wrong?

fawk3s

sophiecentaur
Gold Member
2020 Award
Why not use the proper terms?
Resistance is resistance. Reactance is reactance and Impedance is the complex result of adding the resistance and the reactance. You can't avoid complex quantities if you want to discuss what goes on in LRC circuits. Just bite the bullet and get down to it.
It may just take more than two minutes.

Im sorry for using the wrong terms. English is not my native language and so I should have done some research. My mistake.

But if I understand your post correctly, you understood my question even with the wrong terms.
So the thing is, as the reactances of the capacitor and inductor come closer together, the smaller the impedance becomes. But what I cannot grasp is why isnt this used in a transformer circuit?

berkeman
Mentor
Im sorry for using the wrong terms. English is not my native language and so I should have done some research. My mistake.

But if I understand your post correctly, you understood my question even with the wrong terms.
So the thing is, as the reactances of the capacitor and inductor come closer together, the smaller the impedance becomes. But what I cannot grasp is why isnt this used in a transformer circuit?

In a transformer circuit, you only "see" the leakage inductance, not the magnetizing inductance. The magnetizing inductance links the primary to the secondary, and transforms the secondary load impedance back to the primary side.

In transformer design, you try to keep the leakage inductance small enough so that it does not affect your circuit operation too much.

According to the formula

Z = (sqrt) R^2 + (Xc-Xl)^2

where Z is the overall resistance or the impedance, R is the "wire resistance", and Xc and Xl are the resistances of the capacitor and inductor,
adding a certain capacitor to a certain inductor should lessen the overall resistance.
Say, Xc and Xl were equal. The only resistance in the circuit would be the actual wire resistance.
Or am I understanding the meaning of Z / the overall resistance wrong?

Well, the reactance of a capacitor and inductor depend differently on frequency. The reactance of a capacitor decreases with increasing frequency, while the inductor behaves oppositely.

But I guess at one particular angular frequency, i.e. w = sqrt(1/LC), you would be able to cancel the effect of the two components in series.

sophiecentaur
Gold Member
2020 Award
Well, the reactance of a capacitor and inductor depend differently on frequency. The reactance of a capacitor decreases with increasing frequency, while the inductor behaves oppositely.

But I guess at one particular angular frequency, i.e. w = sqrt(1/LC), you would be able to cancel the effect of the two components in series.

The reactance of a capacitor is 1/wC. That gets less as the frequency increases!! Vice versa for an inductor.

Also, it is common to resonate primary and secondary circuits in IF transformers. This is when they are used as filters, though.

The reactance of a capacitor is 1/wC. That gets less as the frequency increases!! Vice versa for an inductor.

That's exactly what I wrote In a transformer circuit, you only "see" the leakage inductance, not the magnetizing inductance. The magnetizing inductance links the primary to the secondary, and transforms the secondary load impedance back to the primary side.

In transformer design, you try to keep the leakage inductance small enough so that it does not affect your circuit operation too much.

So basically, there would be no point to it because the design is already close-perfect. Thats what I figured, but say in a very poorly designed transformer, would there be a point in adding a capacitor to help reduce the reactance of the system when the AC going through the system is with a determined stable frequency?

sophiecentaur
That's exactly what I wrote 