# Transformers - Variation in Current, EMF and Magnetic FLux

#### elemis

This question about the variation of the aforementioned quantities in a transformer.

Now according to me and my knowledge of electricity this is how I feel it should play out :

If the input current were a sine curve that varies with time then :

Input voltage = cosine curve i.e. it is ahead of input current by 90 degrees.

Magnetic Flux = sine curve with same period as input voltage but LARGER amplitude.

Output voltage = out of phase with input voltage by 180 degrees.

Output current = this is where I'm faltering and I'm having issues....

Could someone please confirm what I've said is correct and help me with the bit in bold ?

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#### elemis

Could someone also confirm if voltage = rate of change of current with time ?

Bump.

#### psparky

Gold Member
Hmmmmmm....interesting question.

I don't know the exact answer...but will just throw out some thoughts.

I know if you have a purely resisitive load hooked to a transformer.....the voltage and current appear to be in perfect phase on the secondary.....and primary. But as you are saying...the primary and secondary should be out of phase by 180 degrees since the secondary pumps current the other direction.

But the coil's inductive property says it will lag the current behind the voltage......

I'll be interested to see what the smart guys have to say.

#### Carl Pugh

Are you considering a ideal transformer with a load
or
A NON ideal transformer with no load?

#### elemis

Are you considering a ideal transformer with a load
or
A NON ideal transformer with no load?
You have to understand that I'm an A Level student i.e. the equivalent of an American High School student.

Anyways, we've only been considering IDEAL transformers where we are told the is a Primary coil voltage and secondary coil voltage. We are never shown the presence of a load.

So, I'm guessing I want to know about an IDEAL transformer with NO load ?

#### gerbi

Gold Member
You have to understand that I'm an A Level student i.e. the equivalent of an American High School student.
In that case, this question should be answered in Homework section.

Anyway.. In academic approach an "ideal transformer" means that:
- we neglect the resistance of the windings -> the transformer has efficiency equal to 1 (Pin = Pout),
- we assume that the schematic of transformer contains only two coils (primary and secondary),
- current and voltage on both sides are connected only by turn ratio of coils,
- all waveforms (current, voltage, flux) are assumed to be sinewave,

Flux can be calculated from Faraday's law of induction. In this case (only inductances in schematic of transformer) we have:

Uprimary - 0 deg
Flux and I primary - 90 deg
U secondary - 180 deg
I secondary and counter flux - 270 deg
Magnetic Flux = sine curve with same period as input voltage but LARGER amplitude.
?
Please tell me, how can You compare amplitude of flux and voltage ? Volts vs Webers ? Amplitude of flux depends on voltage and magnetic circuit as said below:

Induction * Cross.section = Flux = Voltage / (4,44 * Frequency * Turn.ratio)

That's in theory - means BIG simplifications.

#### elemis

In that case, this question should be answered in Homework section.
Well, this isnt a homework question. Its me trying to further my knowledge in the subject.

Anyway.. In academic approach an "ideal transformer" means that:
- we neglect the resistance of the windings -> the transformer has efficiency equal to 1 (Pin = Pout),
- we assume that the schematic of transformer contains only two coils (primary and secondary),
- current and voltage on both sides are connected only by turn ratio of coils,
- all waveforms (current, voltage, flux) are assumed to be sinewave,

Flux can be calculated from Faraday's law of induction. In this case (only inductances in schematic of transformer) we have:

Uprimary - 0 deg
Flux and I primary - 90 deg
U secondary - 180 deg
I secondary - 270 deg
What do you mean by U Primary ? Is that the voltage across the primary coil ? Do you mean 90 degrees ahead of U Primary or lagging behind ?

#### gerbi

Gold Member
What do you mean by U Primary ? Is that the voltage across the primary coil ? Do you mean 90 degrees ahead of U Primary or lagging behind ?
Uprimary is primary voltage (on primary coil).
Leading or lagging ? We consider coils here - currents are lagging.

#### elemis

Uprimary is primary voltage (on primary coil).
Leading or lagging ? We consider coils here - currents are lagging.
To be honest you're only confusing me.

Could you have a look at my post and tell me whether what I've said is correct or wrong ?

#### gerbi

Gold Member
To be honest you're only confusing me.

Could you have a look at my post and tell me whether what I've said is correct or wrong ?
That's why this questions should be answered in Homework section.

Uprimary means voltage measured between both terminals of a coil.

Currents in both windings are 90 deg behind voltages (currents are lagging).

#### Carl Pugh

In an ideal transformer with no load:
There would not be any primary or secondary current.
Magnetic flux would lag the applied voltage by 90 degrees.
Magnetic flux and voltage are in different units, so you cannot say one is larger than the other.
Output voltage phase depends on how the transformer is connected. Some engineers might say that input voltage and output voltage are 180 degrees out of phase. I consider output voltage and input voltage in phase.

#### psparky

Gold Member
In an ideal transformer with no load:
There would not be any primary or secondary current.
Magnetic flux would lag the applied voltage by 90 degrees.
Magnetic flux and voltage are in different units, so you cannot say one is larger than the other.
Output voltage phase depends on how the transformer is connected. Some engineers might say that input voltage and output voltage are 180 degrees out of phase. I consider output voltage and input voltage in phase.
They are techinically out of phase by 180 degrees.....but who cares? So what you are saying is more or less true. When you hook up your load to your secondary....the voltage and current are in phase....and the reference point of you voltage is what it is. Referring back to the primary phase of the voltage doesn't do you any good unless you are playing with math. In the field....this info won't help you.

To elemis.......since you are at a high school level....keep things simple. The turns ratio.....power in = power out.....and the formula for computing the resistance from the secondary back to the primary should be all you need at this point. Until these things are mastered.....don't move on quite yet.

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#### jim hardy

Gold Member
2018 Award
Dearly Missed
Some high schools teach enough calculus to have covered that derivative of a sinewave is a cosine wave.

My high school did not. At least before 12th grade.
Our Electronics teacher taught us 10th grade boys that sine and cosine waves are same shape but shifted 90deg and we worked the circuit problems using operator j which shifted 90 degrees. So two 90 degree phase shifts = 180 deg phase shift, which reverses polarity, which is same as multiplying by -1, so operatorj we thought of as √-1. We worked our problems in simple algebra using rectangular and polar notation . Became skilled at conversions by slide rule .

We had one guy in class who was somewhat of a prodigy and he worked the problems via math resembling Eueler's identity . He was way ahead of us ordinary kids.

So if you haven't taken calculus yet that's okay, you will. Meantime i'm sure you are aware the cosine wave is a plot of the slope of a sine wave and vice versa.

Your understanding of the transformer is pretty good.
Re polarity we indicate polarity on a schematic diagram by dots on the ends of the windings that go positive at same time. In practice you find it with a battery and multimeter.

Point of all this - you seem to have a good start !
Curiosity - are you taking an electronics course in high school or is this your own hobby?

old jim

#### elemis

Some high schools teach enough calculus to have covered that derivative of a sinewave is a cosine wave.

My high school did not. At least before 12th grade.
Our Electronics teacher taught us 10th grade boys that sine and cosine waves are same shape but shifted 90deg and we worked the circuit problems using operator j which shifted 90 degrees. So two 90 degree phase shifts = 180 deg phase shift, which reverses polarity, which is same as multiplying by -1, so operatorj we thought of as √-1. We worked our problems in simple algebra using rectangular and polar notation . Became skilled at conversions by slide rule .

We had one guy in class who was somewhat of a prodigy and he worked the problems via math resembling Eueler's identity . He was way ahead of us ordinary kids.

So if you haven't taken calculus yet that's okay, you will. Meantime i'm sure you are aware the cosine wave is a plot of the slope of a sine wave and vice versa.

Your understanding of the transformer is pretty good.
Re polarity we indicate polarity on a schematic diagram by dots on the ends of the windings that go positive at same time. In practice you find it with a battery and multimeter.

Point of all this - you seem to have a good start !
Curiosity - are you taking an electronics course in high school or is this your own hobby?

old jim
Actually, this is simply part of the A Level (British Curriculum) syllabus for Physics.

#### Carl Pugh

I know that this is starting an argument like discussing politics or religion, but what the heck.

I say the polarity of the input winding is the same as the output winding because.
You can wind a transformer with two wires at the same time. (bifilar winding)
The start of both wires can be connected together and the end of both wires can be connected together.
This winding can be used as the primary (or secondary) of the transformer.
Thus both wires have the same polarity.
Now you can disconnect one wire and have a secondary. The polarity hasn't changed, so the polarity of the primary and the secondary is the same.

#### jim hardy

Gold Member
2018 Award
Dearly Missed
Actually, this is simply part of the A Level (British Curriculum) syllabus for Physics.
I was in high school in 1961-1964.

Sounds like your physics is more comprehensive than was ours.
That's good. This is the age of technology and i believe education system should prepare us for the world we live in. The high school i attended was experimenting with that concept. I was very fortunate. It gave me a running start at engineering school.

We also studied a year of English Literature. Does your syllabus include any American lit ?

old jim

#### elemis

I was in high school in 1961-1964.

Sounds like your physics is more comprehensive than was ours.
That's good. This is the age of technology and i believe education system should prepare us for the world we live in. The high school i attended was experimenting with that concept. I was very fortunate. It gave me a running start at engineering school.

We also studied a year of English Literature. Does your syllabus include any American lit ?

old jim
Well then, that's a loooong time ago :D

The British curriculum is very different in the sense we have a year 12 and 13.

Where an American child is doing the SATs we do the A Level.

At A Level you can choose any number of subjects of any combination to be examined under. Obviously, if you're going to study Chemistry (like me) you would do Chemistry, Physics, Maths and (if you wanted to) Literature (I did Further Maths instead).

#### elemis

I was in high school in 1961-1964.

Sounds like your physics is more comprehensive than was ours.
That's good. This is the age of technology and i believe education system should prepare us for the world we live in. The high school i attended was experimenting with that concept. I was very fortunate. It gave me a running start at engineering school.

We also studied a year of English Literature. Does your syllabus include any American lit ?

old jim
Out of interest, what happened to that high school prodigy you mentioned ? Did he go on to do something great ?

#### gerbi

Gold Member
I know that this is starting an argument like discussing politics or religion, but what the heck.

I say the polarity of the input winding is the same as the output winding because.
You can wind a transformer with two wires at the same time. (bifilar winding)
The start of both wires can be connected together and the end of both wires can be connected together.
This winding can be used as the primary (or secondary) of the transformer.
Thus both wires have the same polarity.
Now you can disconnect one wire and have a secondary. The polarity hasn't changed, so the polarity of the primary and the secondary is the same.
This is not true with all transformers.

I think that physics is not like a religion or politics. Laws works always the same way no matter what. No matter what each engineer say or think, we must obey to the same laws.

Imagine this bifilar winding - same polarity on both wires. Now switch terminals on one of the windings.. and we have voltages in counterphase (180 deg).

Any further discussion about primary and secondary voltages in phase or in counterphase should start from stating how windings are connected. This is the real issue here.

And sorry guys.. but problem of winding connection is one of the main issues when connecting transformer to the grid. Don't underestimate it and don't tell this is only important while doing math.

Little summary as threat starter wished.

Input voltage = cosine curve i.e. it is ahead of input current by 90 degrees.?
True
Magnetic Flux = sine curve with same period as input voltage but LARGER amplitude.
Not true. Flux is in phase with primary current and in counterphase of secondary current. Do not compare amplitudes of different physical quantities.
Output voltage = out of phase with input voltage by 180 degrees.
Basically true (for an ideal transformer) but can be 0 deg when You simply switch terminals.
Output current = this is where I'm faltering and I'm having issues....
Output current is in counter phase to primary current and 90 deg behind secondary voltage.

Edit: This all applies to ideal transformer only with pure inductive load.

As stated in posts below - angle between current and voltage depends solely on load as an ideal transformer has no resistance and no reactance (there is no leakage flux).

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#### jim hardy

Gold Member
2018 Award
Dearly Missed
Well, we have to separate magnetizing current from load current.

an IDEAL transformer could have zero magnetizing current

but a real one must have some.

Magnetizing current is in phase with flux and 90deg out of phase with primary voltage

But load current has phase determined by nature of the load. If load is resistive then load current is in phase with terminal voltage. Observe that load current flows in both primary and secondary , in proportions set by turns ratio of course.

My mental model uses an ideal transformer with infinite indutcance hence it draws no magnetizing current.
Some people prefer to use in their model an ideal transformer with finite inductance and consider the magnetizing current.
Note that if you do that your ratio of primary to secondary currents will be different than the ratio of primary to secondary turns by the amoount of magnetizing current. That's because magnetizing current flows only in primary. It is small compared with load current so is usually neglected in power transformers. It is accounted for in current transformers by tweaking the turns ratio.

So i'd have to raise my eyebrows at this one :
Output current is in counter phase to primary current and 90 deg behind secondary voltage
.

old jim

#### gerbi

Gold Member
an IDEAL transformer could have zero magnetizing current
It has no magnetizing current since only elements of transformer schematic are the coils (there is no transverse branch in schematic). Let's keep it this simple here.

But load current has phase determined by nature of the load. If load is resistive then load current is in phase with terminal voltage. Observe that load current flows in both primary and secondary , in proportions set by turns ratio of course.
That's true, ofcourse. Phase between voltage and curent (both primary and secondary) are determined by the load since transformer acts just like a simple 'electrical gear' (divides and multiplies current/voltage by turn ratio).

That's because magnetizing current flows only in primary.
Not true in practice. In short.. Power transformers with star connected winding have usually secondary connected in delta (or have third, 'compensating' winding) so higher harmonic magnetizing currents can circulate (flux in core is more sinusoidal then).

So i'd have to raise my eyebrows at this one : .
old jim
What would be flux look like if the currents wouldn't be in counterphase ?

About that 90deg - got that now. Ideal transformer has no resistance and no reactance (there is no leakage flux). It's simply a 'electrical gear'. So phase shift between current and voltage on primary side (secondary side as well) will depend only on load. Thanks for that jim and sorry for my mislead.

#### jim hardy

Gold Member
2018 Award
Dearly Missed
Not true in practice. In short.. Power transformers with star connected winding have usually secondary connected in delta (or have third, 'compensating' winding) so higher harmonic magnetizing currents can circulate (flux in core is more sinusoidal then).
Ahh yes, the tertiaries. Often used to power the cooling fans and oil circulators.
Good one !!

So i'd have to raise my eyebrows at this one : (.....""counter phase to primary current and 90 deg behind secondary voltage....) ""'

What would be flux look like if the currents wouldn't be in counterphase ?
it's the 90 deg i was questioning not the counterphase. My bad, Big ten-oops there.

Thanks !

old jim

Elemis - the prodigy kid got a scholarship to a big name unversity. I lost track of him. In fact have forgotten his last name , i knew him only as Fabio. I will see if i can find my yearbook and track him down. Thanks !

#### FOIWATER

Gold Member
i see what you mean now, what i wrote would only constitute an inductive load. obviously that's not the only case

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#### gerbi

Gold Member
Then your secondary current is always ninty degrees behind your output voltage regardless of reference
Please feed us with math that stands behind this because now I have some big dilemma.
- we are discussing ideal transformer,
- there is no resistance in ideal transformer,
- there is no leakage reactance in ideal transformer (as there is no leakage flux),
- coils in schematic of ideal transformer indicates perfect magnetic coupling.

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