# Electromagnetic induction in transformer

## Main Question or Discussion Point

Hello!I would like to ask about Electromagnetic induction in transformer.As we learn that an alternating voltage is connected to the primary coil,the alternating current in the primary coil produces a magnetic flux linkage with the secondary coil which constantly changes.$$\phi$$=magnetic flux linkage in each coil of primary and secondary coil
and the way that this formula(turn ratio)work out.Considering the transformer is ideal,why "the magnetic flux linkage in primary coil is same to secondary coil-using to work out the turn ratio formula" this assumption is true?We study of the solenoid that produce the magnetic flux density is affected by the number of turns per unit length of solenoid and yet for transformer,the solenoid is just like primary coil.With constantly changes of magnetic flux,the magnetic flux induced in the secondary coil is $$\phi$$=NBA,B=magnetic flux density from primary coil,there is a 'N' inside the formula,so why should be the magnetic flux linkage in primary coil same as secondary coil?

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Well, the secondary flux and the primary flux, are *almost*, but *not quite* "the same". The core is ferromagnetic material, and its high permeability results in nearly all of the primary flux linking the secondary winding. Of course, the P and S windings have some distance separating them, and the medium is air. A small portion of the primary flux does not link the secondary, and vice versa. These are the leakage fluxes, and leakage inductances.

The flux density is established by the following factors. I'll presume that this is a "voltage" or "potential" transformer, and not a "current" transformer. That is, the primary winding is driven by an independent power source that is "constant voltage*. The amplitude of the constant voltage source (CVS), Vp, the number of primary turns, Np, the core cross sectional area, Ac, and the frequency f, determine the core flux density B.

Ideally all of the core flux links the secondary. Thus the secondary voltage, Vs, is determined by Vp, Np, Ac, f, as well as Ns, the secondary no. of turns. Just as a CVS impressed across a winding can determine the flux density B, so does a flux density B determine the secondary voltage Vs. Faraday's law is bi-lateral. A time changing voltage source results in a time changing flux, as well as vice-versa.

In a nutshell, Vp/Np = Vs/Ns.

Is that clear?

Thank you very much!But I still not very clear with what you have explained.

What is constant voltage?If it is constant voltage have can it have magnetic flux?

My problem is I am only A level standard,still studying,and I don't understand with the frequency that you mentioned,coz I don't know how to use this frequency to relate to flux density.Can you show me your steps in determining the core flux density?

typing error"What is constant voltage?If it is constant voltage how can it have magnetic flux?"

A constant voltage source is an independent source of electrical power that maintains a constant voltage across its terminals. The generators at the power plants that supply our household power are monitored continuously with instruments/microcomputers to assure that the voltage stays constant. To do so requires a constant turbine speed. When load demands increase, more fuel must be burned in order to maintain constant speed/voltage. A CVS wll output a fixed voltage and a variable current. When the load resistance changes, the CVS outputs a different current in accordance with Ohm's law.

Faraday's law is what relates the magnetic flux to the frequency, voltage, core area, and no. of turns. Google "Faraday's law" and the equations should come up. Ampere's law relates the magnetic flux with no. of turns, current, magnetic path length, and core area. A Google search will provide equations that you can use to compute what you need to know.

In the MKS (meter kilogram second) unit system

Bm = (Vp)/(4.443*f*Ac*Np),

where Bm = peak value of magnetic flux density in tesla, Vp = rms value of primary voltage, f = frequency in Hz, Ac = core cross sectional area in meter^2, Np = primary no. of turns.

Does this help?

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Thank you!