# A tale of three inductors

Hyperthetically, say you had three inductors that each were ideal (90 deg lagging each) pf of zero.
So there is a circuit with some current limited supply and you series these inductors up and excite the circuit.
Is it going to look like a capacitor because the total angle is 270o like a capacitor? If so could I use three inductors in parallel with some load like you would use a cap for PF correction?

Cheers

## Answers and Replies

No

Didn't think so, can you elaborate a bit about why?

Didn't think so, can you elaborate a bit about why?
If the circuit load is of inductive character, pf is corrected by capacitor component.
If the circuit load is of capacitive character, pf is corrected by inductor component.

Not that I'm arguing it would work (if it did I'm sure it would have been done) but a synchronous condenser acts like a capacitor (but is magnetic) I was just thinking this might be a bit like that. I just want to understand that although the current would look like it was leading like a capacitor (-90o) it won't work because...

Not that I'm arguing it would work (if it did I'm sure it would have been done) but a synchronous condenser acts like a capacitor (but is magnetic) I was just thinking this might be a bit like that. I just want to understand that although the current would look like it was leading like a capacitor (-90o) it won't work because...
"Sync. condenser" is a rotating machine which has independent excitation.
Combining more inductors in series or paralell just increases or reduces effective inductance. Summing up phase angles like you describe is nonsense.

I know it's 'nonsense' I can feel it wouldn't work, I just want to understand why summing up the phase angles doesn't work, my theory is that it will only asymptotically move the phase angle closer to 900 and not beyond (i.e to 270o) but I'd like some varification or someone else's thoughts on explaining what would happen.

Before you theorize on your own, I'd strongly recommend to study and learn basics of theory of phasors used in linear AC circuits analysis.
Good educational video.

Yeah it would be a good educational video but I'm not learning anything from it.
I"m pretty sure my theory is correct, the way I figure it: they'd probably act like one lumped inductance element, rather than like 'phasor multiplication'.

If you connect impedances Z1 and Z2 in series the resulting impedance is Z = Z1+Z2. I guess you propably knew that so the reason why zoki tried to guide you in the direction of phasors is the fact that when you add imaginary numbers together it doesn't affect the phase angle. Multiplication does but summing doesn't.

Yeah thanks, you're right. At first thought I wasn't concidering them to be like summing the impedance, so yeah, it would be like asymptotically approaching 90deg the more inductors added.

Actually there would be no asymptotical approaching because for ideal inductor the phase angle would always be 90deg and for real inductors the phase angle would still not be assymptotically approaching anything. The phase angle for impedance is tan^-1(imaginary part/real part) so the only thing that matters for phase angle is the ratio between real and imaginary part not the absolute magnitude. The amount of inductance doesn't picture the amount of phase lag but the ability to restrict changes in current. So in a circuit with constant resistance higher inductance doesn't lag more but is able to generate higher voltage in the lag of 90degrees compared to voltage over resistive part. This changes the total phase to lagging direction.

Lets take example where Z1 and Z2 have the same phase angle so you can see it doesn't change. If Z1 would be 5+20j which corresponds the phase angle phase=tan^-1(20/5)=75.96 deg and Z2 = 2.5+10j corresponding phase=tan^-1(10/2.5)=75.96deg then the sum Z1+Z1 would be 7.5+30j which would still be corresponding to phase=tan^-1(30j/7.5)=75.96 deg. Only the magnitudes changed so now resistance and inductance that equals impedance would be higher but the phase would still be the same.

Hopefully this helps more than confuses.

Last edited:
sophiecentaur
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If you connect impedances Z1 and Z2 in series the resulting impedance is Z = Z1+Z2. I guess you propably knew that so the reason why zoki tried to guide you in the direction of phasors is the fact that when you add imaginary numbers together it doesn't affect the phase angle. Multiplication does but summing doesn't.
That says it all.
Otoh, a lumped element transmission line can introduce any phase shift you like - if you make it long enough.

I know it's 'nonsense' I can feel it wouldn't work, I just want to understand why summing up the phase angles doesn't work, my theory is that it will only asymptotically move the phase angle closer to 900 and not beyond (i.e to 270o) but I'd like some varification or someone else's thoughts on explaining what would happen.

I will explain this for you and hopefully put your confusions to rest. The primary intuition for understanding this concept can be found by having a solid understanding of complex numbers. It will come with practice, but let me explain.

Begin with a Cartesian coordinate system, with the X and Y axes. Now take a vector, we know it represents a magnitude and a direction. If you want to break this vector into its individual components then we find that the magnitude of the vector (C) multiplied by the cosine of the angle of the vector from the x axis, is the X component of the vector. If we multiply C by sin(theta), we have the Y component of the vector.

Ok, now with that in mind understand that a complex number, R+jX, is the real (R) part of the number plus the imaginary (jX) part. Now substitue the X axis as the real (R) axis, and the Y axis as the imaginary (j) axis.

Now here is the key: We know that when calculating impedances, resistances do not have a j component and thus are purely real, this means they are only along the R axis; j=0. Now remember the impedances for a capacitor [ -j/(wC) ] and inductor [ jwL ]. Notice they are ONLY imaginary (or usually referred to reactive when speaking of circuits). This means they only extend upon the j axis. Therefore we have +j for inductance, and -j for capacitance, if you think of the j unit vector, depending on the sign of the impedance it will either point up or down. In conclusion, if you only add impedances with the same sign (+ or - j), the direction of the phase angle will only be either +90 degrees for inductance or -90 degrees for capacitance, and you will only be increasing the magnitude of the vector.

Actually there would be no asymptotical approaching because for ideal inductor the phase angle would always be 90deg and for real inductors the phase angle would still not be assymptotically approaching anything....

Lets take example where Z1 and Z2 have the same phase angle so you can see it doesn't change. If Z1 would be 5+20j which corresponds the phase angle phase=tan^-1(20/5)=75.96 deg and Z2 = 2.5+10j corresponding phase=tan^-1(10/2.5)=75.96deg then the sum Z1+Z1 would be 7.5+30j which would still be corresponding to phase=tan^-1(30j/7.5)=75.96 deg. Only the magnitudes changed so now resistance and inductance that equals impedance would be higher but the phase would still be the same.

Thanks, yeah I can visualise that. When I said asymptotically approaching, I was making the shift from the theory of the idea to thinking about it in practice not working, i.e z1 = something_small + j*something_quite_big
thus 3*z1 = z1+z2+z3 = something_still_quite_small + j*something_very_big
so the magnitude has gone up by three and the angle tan^-1(small/very big) has gotten closer to 90, by a bit.

I will explain this for you and hopefully put your confusions to rest. ... In conclusion, if you only add impedances with the same sign (+ or - j), the direction of the phase angle will only be either +90 degrees for inductance or -90 degrees for capacitance, and you will only be increasing the magnitude of the vector.
Certainly some good explinations but I hope what I said explains my negligence was in not mentioning I knew how it would effect the magnitude and an incusion of a realistic phase angle of an inductor.
Thanks for all the comments

I think, Nobody specifically showed what was wrong in the reasoning in the OP, besides saying it is wrong and providing the correct approach. Sorry, if I missed. So I will try.
Hyperthetically, say you had three inductors that each were ideal (90 deg lagging each) pf of zero.
So there is a circuit with some current limited supply and you series these inductors up and excite the circuit.
Is it going to look like a capacitor because the total angle is 270o like a capacitor? If so could I use three inductors in parallel with some load like you would use a cap for PF correction?
Cheers
The current in each of the inductor lags the voltage across each of them by 90 degree, i.e. the inductors be A,B and C, then IA lags VA by 90, IB lags VB by 90 and IC lags VC by 90.
You were thinking like, IB would lag IA by 90 and then IC would lag IB by 90 thereby making it 270 degree altogether , which isn't the case. Current lags voltage by 90, not current.
So, all three voltages will be in phase, and all three currents will be in phase, and the currents will lag voltage by 90, just like an inductor and unlike a capacitor.

I think, Nobody specifically showed what was wrong in the reasoning in the OP, besides saying it is wrong and providing the correct approach. Sorry, if I missed. So I will try.

The current in each of the inductor lags the voltage across each of them by 90 degree, i.e. the inductors be A,B and C, then IA lags VA by 90, IB lags VB by 90 and IC lags VC by 90.
You were thinking like, IB would lag IA by 90 and then IC would lag IB by 90 thereby making it 270 degree altogether , which isn't the case. Current lags voltage by 90, not current.
So, all three voltages will be in phase, and all three currents will be in phase, and the currents will lag voltage by 90, just like an inductor and unlike a capacitor.

Well distilled and said.