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# Transformers: A thought watch

1. The principal of the ratio of the windings of coils demonstrates that Ns/Np=Vs/Vp. Meaning if the secondary coil has 2Np coils, the potential difference between the two ends of the windings on the secondary coil would be 2Vp. However, consider this scenario. If you increase the current in the primary coil by reducing the resistance of the windings in the primary coil, there would be a greater flux generated in the iron core. Therefore there would be a greater rate of change of flux in both and hence there would be a larger pd induced at the secondary coil. This seems to violate the ratio, since now Vs would no longer be equal to 2Vp, it would be slightly larger. I know that this doesn't happen, so where in this thought have I gone wrong? Ohms law tells us that V is proportional to R. Hence if the we have a power supply fixed at V, decreasing the resistance of the windings would increase the current. I have read, however, that because the flux is constant through both coils, the ratio of d[phi]/dt is the same in both cases, hence the ratio of induced emf would be (Npd[phi]/dt)/(Nsd[phi]/dt) where d[phi]/dt cancel and leave us with Np/Ns = Vp/Vs. Does this mean that the emf produced in the secondary coil is independent of the RMS current supplied to the first coil? However, the current in both coils would increase if the RMS current increases due to conservation of energy.
2. (Original post by Protoxylic)
The principal of the ratio of the windings of coils demonstrates that Ns/Np=Vs/Vp. Meaning if the secondary coil has 2Np coils, the potential difference between the two ends of the windings on the secondary coil would be 2Vp. However, consider this scenario. If you increase the current in the primary coil by reducing the resistance of the windings in the primary coil, there would be a greater flux generated in the iron core. Therefore there would be a greater rate of change of flux in both and hence there would be a larger pd induced at the secondary coil. This seems to violate the ratio, since now Vs would no longer be equal to 2Vp, it would be slightly larger. I know that this doesn't happen, so where in this thought have I gone wrong? Ohms law tells us that V is proportional to R. Hence if the we have a power supply fixed at V, decreasing the resistance of the windings would increase the current. I have read, however, that because the flux is constant through both coils, the ratio of d[phi]/dt is the same in both cases, hence the ratio of induced emf would be (Npd[phi]/dt)/(Nsd[phi]/dt) where d[phi]/dt cancel and leave us with Np/Ns = Vp/Vs. Does this mean that the emf produced in the secondary coil is independent of the RMS current supplied to the first coil? However, the current in both coils would increase if the RMS current increases due to conservation of energy.
The equation assumes an ideal transformer. In reality, there is losses of course. You can calculate the power input and output ratio to find the percentage efficiency and add that in, which would counteract this. Most questions will give you the percentage efficiency though, or ask you to find it. The ideal transformer will have no losses at all.
3. (Original post by Phichi)
The equation assumes an ideal transformer. In reality, there is losses of course. You can calculate the power input and output ratio to find the percentage efficiency and add that in, which would counteract this. Most questions will give you the percentage efficiency though, or ask you to find it. The ideal transformer will have no losses at all.
I completely understand that this equation assumes an ideal transformer. My question really was what happens when you increase the current in the primary coil by decreasing the winding resistance to keep V constant. Instinct says that the rate of change of flux should increase in both cases. However, as stated in my previous post, these flux changes seem to cancel and suggest that the pd out is independent of the current in?
4. (Original post by Protoxylic)
I completely understand that this equation assumes an ideal transformer. My question really was what happens when you increase the current in the primary coil by decreasing the winding resistance to keep V constant. Instinct says that the rate of change of flux should increase in both cases. However, as stated in my previous post, these flux changes seem to cancel and suggest that the pd out is independent of the current in?
An ideal transformer has no resistance and no infinite inductance. You can't possibly increase the current by reducing a resistance that doesn't exist, and the induced e.m.f is a maximum due to the infinite inductance.

When you increase the current by decreasing the resistance in a real transformer, you're just making the percentage efficiency higher. The use of a transformer is for power.

If I told you this equation holds for an ideal transformer, does it help answer your question?

Didn't see your last question until now. The current in the secondary coil would be larger, the pd would be the same. Hence, the power in the secondary coil would be larger, due to the power in the primary being larger, via the increased current. Does that answer your question?

Also, did you decrease the resistance in the secondary coil too?
5. (Original post by Phichi)
An ideal transformer has no resistance and no infinite inductance. You can't possibly increase the current by reducing a resistance that doesn't exist, and the induced e.m.f is a maximum due to the infinite inductance.

When you increase the current by decreasing the resistance in a real transformer, you're just making the percentage efficiency higher. The use of a transformer is for power.

If I told you this equation holds for an ideal transformer, does it help answer your question?

Didn't see your last question until now. The current in the secondary coil would be larger, the pd would be the same. Hence, the power in the secondary coil would be larger, due to the power in the primary being larger. Does that answer your question?
Alright, the concepts for a real transformer make sense except for the pd being the same. I know that the pd is the same, but If I think about it in a way that a greater current means a greater flux in the core, hence a greater rate of change of flux through the coil/s. Hence there should be a greater emf produced in the secondary coil. (I know this isn't true, but isn't this line of thought contradicting?)
6. (Original post by Protoxylic)
Alright, the concepts for a real transformer make sense except for the pd being the same. I know that the pd is the same, but If I think about it in a way that a greater current means a greater flux in the core, hence a greater rate of change of flux through the coil/s. Hence there should be a greater emf produced in the secondary coil. (I know this isn't true, but isn't this line of thought contradicting?)
maybe think about this: The constraint on the AC current in the primary doesn't have much to do with the resistance of the primary winding as measured at DC, or shouldn't in real life transformers. most of the energy going in to the primary isn't being turned to heat in the copper.
7. (Original post by Protoxylic)
Alright, the concepts for a real transformer make sense except for the pd being the same. I know that the pd is the same, but If I think about it in a way that a greater current means a greater flux in the core, hence a greater rate of change of flux through the coil/s. Hence there should be a greater emf produced in the secondary coil. (I know this isn't true, but isn't this line of thought contradicting?)
The simplicity of basic transformer equations hide the complexity of their operation.

A transformer cannot operate on d.c. The current in the primary needs to be constantly changing in order to induce a voltage in the secondary winding. That little snippet means Ohms law is not invalidated but you need to think in terms of impedances not resistances.

To get you thinking along the right lines:

Q) What is a back e.m.f?

Q) What is the relationship between e.m.f., back e.m.f. and current in an inductor.

Q) How does an inductor store energy and why is there a phase relationship between the voltage and current in an inductor?

Q) How does the primary current of a transformer somehow know what the secondary load is?
8. (Original post by uberteknik)
The simplicity of transformer equations hide the complexity of their operation.

A transformer cannot operate on d.c. The current in the primary needs to be constantly changing in order to induce a voltage in the secondary winding. That little snippet means Ohms law is not invalidated but you need to think in terms of impedances not resistances.

To get you thinking along the right lines:

Q) What is a back e.m.f?

Q) What is the relationship between e.m.f., back e.m.f. and current in an inductor.

Q) How does an inductor store energy and why is there a phase relationship between the voltage and current in an inductor?

Q) How does the primary current of a transformer somehow know what the secondary load is?
There would be a back emf produced due to the current in the secondary coil producing an opposing alternating electromagnetic field which induces an opposing emf in the primary coil.

E.M.F - back E.M.F = IR hence (e=emf, eb=back emf) eI-ebI=I^2R

I haven't looked at the topic of impedance.
9. (Original post by Protoxylic)
There would be a back emf produced due to the current in the secondary coil producing an opposing alternating electromagnetic field which induces an opposing emf in the primary coil.
Not quite.

The back e.m.f. of the primary is the sum of two components. The first component is independent of the secondary current.

Lenz's law states that this back e.m.f. will oppose any change in the magnetic field of the coil. That will be the case regardless of anything that happens in the secondary winding.

Any current flowing through the load in the secondary circuit will reinforce the direction of current flowing in the primary not oppose it.

In essence, two emf's are produced by the mutual coupling between the windings.

1) is the back emf which opposes the change in the primary magnetic field.

2) a forward emf created by the secondary load current and which reinforces the flow of current in the primary originally created by the primary voltage source.

The two e.m.f.'s sum to produce an actual back e.m.f. which will be at maximum when no current flows in the secondary and minimum when a high current flows in the secondary.

Impedance is simply frequency dependent resistance and is the result of the phase difference between the changing voltage and resultant current flowing in the primary.

Q) Can you see how the composite back e.m.f. will affect the current flowing in the primary such that ohms law for d.c. will not produce the right answer?
10. (Original post by uberteknik)
Not quite.

The back e.m.f. of the primary is the sum of two components. The first component is independent of the secondary current.

Lenz's law states that this back e.m.f. will oppose any change in the magnetic field of the coil. That will be the case regardless of anything that happens in the secondary winding.

Any current flowing through the load in the secondary circuit will reinforce the direction of current flowing in the primary not oppose it.

In essence, two emf's are produced by the mutual coupling between the windings.

1) is the back emf which opposes the change in the primary magnetic field.

2) a forward emf created by the secondary load current and which reinforces the flow of current in the primary originally created by the primary voltage source.

The two e.m.f.'s sum to produce an actual back e.m.f. which will be at maximum when no current flows in the secondary and minimum when a high current flows in the secondary.

Impedance is simply frequency dependent resistance and is the result of the phase difference between the changing voltage and resultant current flowing in the primary.

Q) Can you see how the composite back e.m.f. will affect the current flowing in the primary such that ohms law for d.c. will not produce the right answer?
So let me get this straight; the back emf in the primary coil is due to the changing flux through the primary windings inducing an emf in the opposite direction to the applied emf. And when the current is max at the secondary coil, there is a maximum back emf on the second coil which is a constructive emf in the primary.
11. (Original post by Protoxylic)
So let me get this straight; the back emf in the primary coil is due to the changing flux through the primary windings inducing an emf in the opposite direction to the applied emf.
Yes. Transformers only work with a.c.

One component of the net e.m.f. across the primary coil is produced by the changing flux through the primary which induces a back e.m.f. opposing the current that created it.

Lenz's law is the reason why the d.c. primary winding resistance cannot account for the actual a.c. flow in the primary.

It's also the reason why it takes time for the current to build to a steady state and hence the phase difference where current lags voltage with inductors.

(A coil connected to a d.c. voltage source will achieve a maximum steady state current governed entirely by Ohms law. Thus if d.c. is applied to the transformer primary, when the steady state current and hence maximum core magnetic flux is achieved, no voltage will be induced in the secondary because the flux does not change.

(Original post by Protoxylic)
And when the current is max at the secondary coil, there is a maximum back emf on the second coil which is a constructive emf in the primary.
Not quite.

The induced voltage of the secondary coil creates a current in the secondary coil flowing via the circuit created by the load.

Because the primary back e.m.f. and the induced secondary voltage are created by the same changing magnetic field in the core, they will point in the same direction.

i.e. the secondary coil current creates a second induced e.m.f. in the primary which reinforces the flow of current in the primary. (It may help to think of the secondary coupling to the primary as if the roles were reversed. i.e. the secondary becomes the primary and the primary as the secondary.)

Hence the secondary load current acts to demand more current from the primary power source. This whole process is collectively referred to as mutual coupling.

Other factors simply add to the complexity of operation including: the direction of the windings around the core. Further, the operation of a transformer is frequency dependent meaning the phase relationship between the voltage and current in the windings changes with frequency and waveform shape. On top of that is hysteresis of the magnetic materials. Then there are the core and winding losses created by it's physical construction!

(As I said, transformers are at face value simple in operation but deceptively complex in reality)

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Updated: January 16, 2015
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