# Is there any Phase difference between the current in primary and secondary coils of a transformer?

Is there any Phase difference between the current in primary and secondary coils of a transformer?

If I draw the diagram of a transformer, and try to find-out the direction of current using Lenz's law; if I keep the coiling-pattern of primary and secondary coils Same (Say both as righthand-screw, or both as Lefthand-screw); I'm getting an 'opposite', i.e. 180-degrees phase-shifted currents in the 2 coils.

is it the case indeed?

However I do-not know, in which-way Lenz's law acts in transformer; because the law states the induced current will try to hinder the cause. but when the secondary circuit of a step-up transformer turned On (closed) , so-far I've know , the current in primary-coil goes-up

P.S.

However, since Amount of Induced-current depends upon CHANGE-rate of magnetic field (Faraday's law), => Amount of current induced in a secondary coil (at a moment), is proportionate with CHANGE RATE of current of the Primary coil;

&

NOT on the CURRENT in primary coil directly (though it apparently seems from the graph). So, same phase-state of primary coil and secondary coil means, in AC, the Graph for Current, and the graph for Change-rate of current, is same. I want to know also, am I right? because, if it was not, then surely a phase difference would found.

• The phase shift between primary and secondary voltage is neglible. If it has 0 or 180 degrees is only due to secondary winding orientation. Apr 25, 2016 at 12:37
• Jul 6, 2016 at 11:30

This answer explains that for an unloaded secondary, the natural phase relationship between primary voltage and secondary voltage is is zero degrees.

It therefore follows that if there is a secondary load current (due to a resistive load), the current in the primary due to that secondary resistive load must be 180 degrees out of phase with the secondary load current i.e. as current flows into the primary, current flows out from the secondary.

This of course is for an ideal transformer and a resistive load.

If you ignore the leakages and magnetization inductance of the transformer, and the load is reactive, then there will be a 90 degrees phase shift.

Bringing in leakage inductance and DC coil resistance will/can muddy the waters. Bringing in magnetization inductance muddies the water a bit more.

The low frequency transformer equivalent circuit is this: -

As you should be able to see, if you considered all the leakages, magnetization inductance and losses and then added a semi-reactive load, the phase angle is quite complex to calculate.

However I do-not know, in which-way Lenz's law acts in transformer; because the law states the induced current will try to hinder the cause.

Strictly speaking, it is voltage that is induced and any current that flows is subject to the that voltage, the load and the leakage inductance.

but when the secondary circuit of a step-up transformer turned On (closed) , so-far I've know , the current in primary-coil goes-up

In normal usage, for a voltage transformer it is non-ideal to consider the secondary being short circuited. However, it makes no difference to the phase angle providing you obey the rules inherent to the model.

• I'm saying that it makes no difference to the phase angle (phase angle is still 180 degrees). It looks like you may have removed words in your question that prompted me to say this..... Where did I make this confession BTW? May 17, 2016 at 13:44
• The yellow box? "However I do-not know, in which-way Lenz's law acts in transformer; because the law states the induced current will try to hinder the cause." May 17, 2016 at 13:49
• Hehe - that's a quote I took from your question LOL May 17, 2016 at 13:50
• Oh I'm very sorry. It was quotation from my question, that was discussed part by part. I Misunderstood it. May 17, 2016 at 13:55

Is there any Phase difference between the current in primary and secondary coils of a transformer?

It depends on 1) the reference direction chosen for the currents of each coil, and 2) the spatial orientation of the two windings; also, the phase shift can change depending on whether the transformer is considered as ideal or real. With respect to point #1, remember that, just because a current is labeled as $$\i(t)\$$ in a circuit diagram, with an assigned reference direction (for example, from node A to node B), it doesn't necessarily mean that the numerical value of the current is positive at a given instant, i.e. that the current is actually flowing from node A to B. With respect to point #2, since you said

If I draw the diagram of a transformer, and try to find-out the direction of current using Lenz's law; if I keep the coiling-pattern of primary and secondary coils Same (Say both as righthand-screw, or both as Lefthand-screw) [...]

there's no ambiguity in the orientation of the coils; actually that's the typical construction assumed when explaining the operation of a transformer; the following construction has the two coils oriented in the same direction (i.e. additive spatial orientation), as you assumed:

Going back to point #1, I'll assume the reference directions of the primary current $$\i_1(t)\$$ and the secondary current $$\i_2(t)\$$ in a way that's intuitive. Suppose that during some time interval $$\\Delta t\$$, a positive current entering the upper terminal of the first coil, denoted by $$\i_1(t)\$$, is increasing, as shown below. Then, applying the RHR for coils, we get that the flux in coil 1 has its north pole above, and so the flux due to $$\i_1(t)\$$ is in clockwise direction. An EMF is induced in coil 2, and assuming a passive element (e.g. a load) is connected to that coil, then a current $$\i_2(t)\$$ is also induced in coil 2. Applying Lenz's law and once more the RHR, we get that $$\i_2(t)\$$, assumed positive during the interval $$\\Delta t\$$, has a direction such that it exits the upper terminal of the second coil, as shown below (the flux due to $$\i_2(t)\$$ is not shown).

Now, since we're assuming that all events happen instantly (valid for lumped elements), whenever $$\i_1(t)\$$ changes, then the flux due to it and thus $$\i_2(t)\$$ will also change. Therefore, for the reference directions chosen above, $$\i_1(t)\$$ and $$\i_2(t)\$$ are in phase. If we had defined the secondary current as entering the upper terminal of coil 2, which we can call as $$\i_2'(t)\$$, then $$\i_2'(t)=-i_2(t)\$$, and so we get that $$\i_2'(t)\$$ is 180 degrees phase-shifted with respect to $$\i_1(t)\$$ (keep in mind the instantaneous numerical value of $$\i_2'(t)\$$ will be negative when $$\i_1(t)\$$ is positive).

If the winding orientation of the two coils were opposing, then the result would've been different. Also, if the transformer is considered as real, there'll be some additional phase shift due to the phenomena ignored in the ideal transformer.