About the I1N1 = I2N2 equation

I have a silly question about this equation which is very frequently used in ideal transformer relations. If I draw the electrical equivalent circuit of the core, then the MMFs of 2 coils N1I1 would cancel N2I2 right? And hence, there would be zero flux in the core, right? And zero flux would ensure no voltage induced in the secondary side. Could anyone resolve this question?

3 Answers

There are two distinct currents that flow into the primary of a non-ideal transformer; one is related (by the turns ratio) to the secondary load current and, the other, is due to the applied primary voltage and the associated magnetization inductance.

• Primary and secondary load currents create equal and opposite magneto motive forces

• The magnetization current flows in the primary and, has nothing to do with load current

• Magnetization current is due to the applied primary voltage and the primary inductance

• In fact you can regard it as the current that flows in the primary with the secondary totally unwound and disconnected

• For an ideal transformer we sometimes un-idealise the magnetization current i.e. we assume the primary inductance is not infinite

• Or sometimes we assume the magnetization inductance is infinite (depends on what we are trying to model of course)

About the I1N1 = I2N2 equation

That's the equation of a totally ideal transformer. There is a magnetic field that induces a secondary voltage but, it's value is indeterminate for an infinite number of turns and zero magnetization current i.e. $$\\infty \times 0\$$ = indeterminate.

It's the problem of cause and result. N2I2 is not driven by current source, thus, it's not making magnetic field flux.

• External current source makes current for N1I1
• N1I1 makes the magnetic field in the core
• The changing magnetic field makes N2I2, now N2I2 becomes a current source.
• The N2I2 current source makes the current of the secondary circuit.
• Hi, can you please please explain/provide reasons for this sentence: N2I2 is not driven by current source, thus, it's not making magnetic field flux.? Commented Feb 10, 2023 at 17:53

Well, zero net flux in an ideal transformer is like zero net voltage across an ideal conductor. It doesn't mean that there is no output voltage (or no current through the ideal conductor), it merely means that there is no waste. If you try calculating the net results from the waste using the idealisation that there is no waste, you'll not get anywhere.

Drawing the flux off via the secondary coils is important for some transformers: for example, operating a tube amp without load can blow the output stage when the output transformer gets saturated and loses most of its differential inductivity.