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Old May 13th 2015, 06:56 AM   #1
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Inductor in transformer

In an inductor, a current waveform 90 degrees out of phase with the voltage waveform creates a condition where power is alternately absorbed and returned to the circuit by the inductor. If the inductor is perfect (no wire resistance, no magnetic core losses, etc.), it will dissipate zero power.

I wonder how this will change in the case of transformer. Suppose the primary and secondary coils are of zero resistance and the core is perfectly ferromagnetic, what should be the phase different between the voltage and current in the primary coil? Power is delivered to the secondary circuit so it should not be absorbed by the primary voltage source as in the case of pure inductor.
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Old May 14th 2015, 09:51 AM   #2
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Before you tackle a transformer with a secondary load are you happy with the (phase) relationships for an unloaded transformer?

If you look around the web you will find the phasor diagrams drawn in lots of different ways so it can be quite confusing.
Tjis is because it depends on what you choose for your x axis reference phasor.

The most logical way is to choose the magnetic flux as it is common to both primary and secondary.
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Old Jun 5th 2015, 08:44 AM   #3
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Originally Posted by studiot View Post
Before you tackle a transformer with a secondary load are you happy with the (phase) relationships for an unloaded transformer?

If you look around the web you will find the phasor diagrams drawn in lots of different ways so it can be quite confusing.
Tjis is because it depends on what you choose for your x axis reference phasor.

The most logical way is to choose the magnetic flux as it is common to both primary and secondary.

May I ask do you really understand the question?
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Old Jun 5th 2015, 09:28 AM   #4
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May I ask do you really understand the question?
Only perhaps since you have not specified which voltages you are comparing phases with which currents.

That is why I asked if you had seen any phasor diagrams.

There are two voltages associated with the primary inductor and two currents in the case of a loaded transformer.

It is usual to compare the phases not with voltage v current, but using the magnetic flux as the base.
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Old Jun 5th 2015, 09:31 AM   #5
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Originally Posted by studiot View Post
Only perhaps since you have not specified which voltages you are comparing phases with which currents.

That is why I asked if you had seen any phasor diagrams.

There are two voltages associated with the primary inductor and two currents in the case of a loaded transformer.

It is usual to compare the phases not with voltage v current, but using the magnetic flux as the base.
But there must be some phase differences other then 90 degrees, otherwise how power is consumed?
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Old Jun 5th 2015, 09:40 AM   #6
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I am fixing some computers at the moment, but I will draw a phasor diagram that explains the phases for a loaded and a nonloaded transformer later this evening, given ideal wiring etc. And yes, there are phase differences other than quadrature for the loaded case.
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Old Jun 5th 2015, 02:38 PM   #7
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OK so here are some phasors Note these are for a no load = open circuit secondary.
So there is a secondary voltage EMF (E2), but no secondary current.

As noted before the magnetic flux in the core is common to both primary and secondary windings so we take that as the reference (x axis) phasor phi as shown if fig1

The applied voltage (Vapp) leads the primary current (Io) by an angle theta as shown in figure 3. Theta is nearly 90 degrees.

The primary current has two components. There is a reactive or magnetising current in the primary causing magnetisation (Ir) which is in phase with the flux and supplies reactive power to the magnetic field, and an active current (Ia) in phase with the applied voltage as shown in fig 2. The active current is the result of eddy current losses in the core, resisitive losses in the windings and hysteresis losses in the core.

So even with ideal windings and no eddy currents Ia will never be quite zero because of hysteresis (see second diagram).

But I mentioned a second voltage as well as two currents.
Fig4 shows that not only is there voltage V applied to the primary but because the primary is immersed in the magnetic field there is also an EMF Ep generated in it.
And this Ep is exactly 180 lagging the applied voltage.
Since the secondary is immersed in the same field it too has an induced EMF Es, in phase with Ep.
With an open secondary Ep is as near as dammit equal but opposite to the applied voltage.

In reality because of hysteresis although the applied voltage might be a sinewave, the primary current is nothing like a sinewave as shown in the second diagram. However the peak of the (distorted) primarary current still occurs at the peak of the magnetisation curve.
Attached Thumbnails
Inductor in transformer-transformer5.jpg   Inductor in transformer-transformer4.jpg  

Last edited by studiot; Jun 6th 2015 at 01:21 AM.
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Old Jun 5th 2015, 02:41 PM   #8
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Here are some alternative viewpoijts and some interesting experiments

Doyou wish to proceed to the phasors for a loaded transformer?
Attached Thumbnails
Inductor in transformer-transformer1.jpg   Inductor in transformer-transformer2.jpg   Inductor in transformer-transformer3.jpg  
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Old Jun 8th 2015, 07:25 AM   #9
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Originally Posted by studiot View Post
Here are some alternative viewpoijts and some interesting experiments

Doyou wish to proceed to the phasors for a loaded transformer?

Thanks for your effort. I'd be glad if you can also provide the phasors for a loaded transformer.
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