# Magnetic flux and current directions of transformer

#### goodphy

Hello.

Let's take a transformer picture first.

The basic equation explaining how the transformer work is the equation of Faraday's law of induction.
$$\begin{array}{*{20}{c}} {{V_P} = - {N_P}\frac{{d{{\rm{\Phi }}_B}}}{{dt}}\;\;\;\;\left( 1 \right).}\\ {{V_S} = - {N_S}\frac{{d{{\rm{\Phi }}_B}}}{{dt}}\;\;\;\;\left( 2 \right).} \end{array}$$ A current in the primary winding IP1 generates B-field (magnetic field) B1 which induces a current in the secondary winding IS1 . IS1 induces another B-field B2 which induces a new current in the primary IP2. IP2 also induces another B-field B3 which induces a new current in the secondary IS2 and so on.

So...I think that the magnetic flux Φ in above equations is a sum of all induced magnetic field B1 + B2 + B3 ... multiplied by a cross-section of the magnetic core. Could you tell me whether or not I'm right on this?

And when I think about Lenz's law, current directions in the attached picture is wrong. The currents must be out of phase or opposite in directions in this picture. In order for currents to be in phase, one of the winding direction must be inverted. For example, in the primary winding, the winding should be done from back side to front side of the core (front side is the side facing reader) to achieve in-phase currents. Could you also confirm my opinion?

Thanks for reading my post and I'm waiting for any replies.

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#### Hesch

Gold Member
A current in the primary winding IP1 generates B-field (magnetic field) B1 which induces a current in the secondary winding IS1

n/dt does not induce a current, but a voltage.
Say that the secondary winding is unloaded, no current at all will pass the secondary winding.

#### jim hardy

Gold Member
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Current makes magnetomotive force MMF, amp turns .
Flux B that flows around the core is MMF/Reluctance of the core.
Flux induces voltage not current, as Hesch points out.

Currents in both Primary and Secondary windings make MMF's. Flux is ΣMMF's / Reluctance of core.

Some authors pretend there is more than one flux flowing and use sum of those fluxes instead, and that is their choice but they should define their method and terms up front.
I prefer to think in terms of summed MMF's because it's easier to account for nonlinear reluctance of the core(and other magnetic effects) in your thinking..

old jim

Last edited:

#### cnh1995

Homework Helper
Gold Member
So...I think that the magnetic flux Φ in above equations is a sum of all induced magnetic field B1 + B2 + B3 ... multiplied by a cross-section of the magnetic core.
No.
A current in the primary winding IP1 generates B-field (magnetic field) B1 which induces a current in the secondary winding IS1 .
As Hesch said earlier, primary magnetic flux induces voltage and not current.
IS1 induces another B-field B2 which induces a new current in the primary IP2.
Right and it is called the 'reflected load current'. This reflected current Ip2flows such that Np*Ip2=Ns*Is.i.e. mmf due to Ip2 exactly cancels out the mmf due to secondary current and this keeps the flux in the core constant. There is no B3, B4 and so on.

A current in the primary winding IP1 generates B-field (magnetic field) B1
This current is called as 'magnetizing current'. As long as primary voltage (rms) and frequency are constant, this magnetizing current is constant irrespective of the load on the secondary.

Edit: The great old Jim got there before me!

#### jim hardy

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And when I think about Lenz's law, current directions in the attached picture is wrong. The currents must be out of phase or opposite in directions in this picture.
Are you sure about that ?
Looks to me like currents flowing in directions shown create opposing primary and secondary MMF's, both up by right hand rule,
which is how transformers work.

Current is pushed into primary by source
current is pushed out of secondary into load.

#### jim hardy

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Sorry cnh, had i known you were on it i'd have held back.

#### cnh1995

Homework Helper
Gold Member
Sorry cnh, had i known you were on it i'd have held back.
Your explanations are way better than mine (and full of interesting anecdotes). It is a great experience to learn from an expert like you!

#### jim hardy

Gold Member
2018 Award
Dearly Missed
There's a time for old guys to step aside and let youth run ahead.
It makes us happy . Like maybe we helped a little.

Keep up your good work !

"Magnetic flux and current directions of transformer"

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