# Dynamics of ideal transformers

Suppose I have the following ideal transformer circuit:

According to the textbook that I was reading (Fundamentals of. Electric Circuits by Charles K. Alexander), V1/V2 = 1/n and I1/I2 = n. Does it imply that, for ideal transformers, V1 and V2 are in phase with each other, whereas I1 and I2 are 180 degrees out of phase? If so, can anyone explain why this is the case?

Suppose the load of the secondary circuit is a resistor, then V2 and I2 are in-phase with each other. Since I1 is 90 degrees out of phase with V1 (which is in-phase with V2). Shouldn't this mean that I2 and I1 are 90-out of phase?

The article from http://www.allaboutcircuits.com/textbook/alternating-current/chpt-9/mutual-inductance-and-basic-operation/#02310.png mentioned about 90-degrees and 180-degrees out of phase. However, after reading several dozen times, I still do not understand the exact dynamics of a transformer. Can anyone please explain the basic working principle of a transformer?

Thank you very much.

I always considered that the currents are in phase but looking at your schematic I can see that on the primary current is entering at the dot end while on the secondary it is leaving at the dot end and feeding the load. I suspect that this is what causes them to be out-of-phase in the analysis.

I think that you have correctly explained the other aspects in your question.

I1 is 90 degrees out of phase with V1

Only that part of the primary current that magnetizes the core is 90 degrees out of phase; the part of the primary current that is due to the secondary load is a different thing entirely. You are getting mixed up between magnetization current and load current. Look at this idealized core with a single turn: -

Current Im flows when voltage is applied. It is 90 degrees out of phase with the voltage because it's a pure inductance. If that single turn were in fact two closely wound parallel turns you's get this: -

The same overall current flows as per the first scenario because the two individual turns are closely wound. Next slide: -

This may seem like a leap of faith - I'm asking you to believe that when those two turns are disconnected from each other, the voltage on the newly isolated coil is the same amplitude and phase as the "primary" coil. It's not really such a big deal because, if you considered the 2nd scenario and thought that the voltage might be antiphase then the 2nd scenario could never work - the inductance would be zero and infinite current would flow.

Last slide: -

As you can see, if you managed to believe in the 3rd scenario then you have no choice but to recognize that although the voltages are in phase, the currents (due to the load) MUST be anti-phase. Current $I_{LOAD}$ and current $I_S$ are exactly the same in amplitude for a perfect 1:1 transformer but there is always an extra current flowing into the primary called $I_M$ (magnetization current). The magnetization current is always 90 degrees lagging the primary voltage.

• Hi @Andy, thanks for the answer. So I1 in my circuit diagram = Im + Iload, where Im is 90-out of phase with V1 and Iload is 180-out of phase with V1. I1 happens to be 180-out of phase with Is (which is the same as I2 in my circuit above), is my interpretation right? If this is the case, then I understand why I1 and I2 in my circuit diagram are 180-out of phase.
– TSP
Dec 26, 2015 at 14:25
• A second thought, if I1 and I2 are 180-out of phase, then I1 should also be 180-out of phase with V1. How can I1 = Im + Iload be 180-out of phase with V1 (unless Iload is infinitely large)?
– TSP
Dec 26, 2015 at 14:33
• Both of your comments are incorrect. Forgetting Im, for power to be transferred to the load resistor, power must be allowed into the transformer therefore the primary current (ignoring Im) is in phase with the primary voltage. If this wasn't true you don't have power going into the transformer and no power gets to the load. Imagine it was a magic black box sat between input terminals and output load and then I told you that the black box was in fact two conductors (no magnetics) joing the top left terminal with the top right terminal and ditto the bottom terminals. Dec 26, 2015 at 15:49
• That black box represents a perfect transformer with infinite primary magnetization current. All we are doing when we have a finite mag inductance is seeing that there is an extra current into the primary that has nothing to do with the secondary. Dec 26, 2015 at 15:51