# Resulting magnetic flux in the core of a transformer

#### HeleneFR

In a transformer, let's say we have:
I1, I2 - currents through the primary and secondary winding
V1, V2 - voltages
N1, N2 - number of turns
F1, F2 - magnetic fluxes through core, produced by the currents I1 and I2 (they are opposing...)
R - the reluctance of the core

We have V1/V2 = N1/N2 = I2/I1.
F1=N1*I1/R; F2=N2*I2/R
I think I1 and I2 are in phase too.
That means F1 and F2 are practically equal.
How can we have a nonzero resulting flux through the core? F=F1-F2
If the flux through the iron core is zero, then the cause that produces V2 (variation of the flux) does not exist, then V2=0?
I know I'm wrong, but i don't know where is the mistake...

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#### BvU

Homework Helper
Hello helene,

As you say, the driving force for induction emf is not the flux itself, but the change in the flux. To keep up counteracting F1 with F2, the amplitude of V2 has to be nonzero.

#### Hesch

Gold Member
How can we have a nonzero resulting flux through the core? F=F1-F2
Say that the impedance in the primary coil = Z1. Then the transformer will balance the flux through N1 so that

( Vsupply - dψv/dt ) / Z1 = I1 as for the primary coil when the transformer is unloaded. ( ψv = Flux * N1 ).

I1 is the current needed for magnetizing the core so that this balance is achieved.

Say that I1 is too small, ψv will be too small → the back emf will be too small → the voltage difference ( the parentheses above ) will be to high, so that I1 will increase.

If you load the transformer, I2 will decrease the flux so that I1 must increase to keep up balance.

BvU

#### jim hardy

Gold Member
2018 Award
Dearly Missed
We have V1/V2 = N1/N2 = I2/I1.
F1=N1*I1/R; F2=N2*I2/R
I think I1 and I2 are in phase too.
realize that I1/I2 isn't exactly equal to turns ratio.
There is small magnetizing current to produce flux enough to oppose applied voltage. It flows in primary winding only and is a loss.
But in a power transformer it's quite small compared to load current so is generally ignored. In the golden era of slide rule accuracy(3 digits) it was a quite reasonable approximation.

Have you studied equivalent circuit of a transformer ?
https://en.wikipedia.org/wiki/Transformer

Do you have a lab at school where you could apply variable voltage to a transformer and plot magnetizing current ?

old jim

"Resulting magnetic flux in the core of a transformer"

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