Magnetic Flux: Why Does it Stay the Same?

[hidemi]

Homework Statement

The resistance of the primary coil of a well-designed, 1 : 10 step-down transformer is 1 Ω. With the secondary circuit open, the primary is connected to a 12V ac generator. The primary current is:

A. essentially zero
B. about 12A
C. about 120A
D. depends on the actual number of turns in the primary coil
E. depends on the core material

The answer key says A.

Relevant Equations

Φ = NBA = N ( μ0*n*i)A

I calculated in this way as attached and got the correct answer. However I still wonder why the magnetic flux is the same in both coils, or this presumption is not right.

 

[DaveE]

In a well designed (simple) transformer the magnetic core's job is to contain almost all of the flux and couple it into all of the windings. This works because it has very high permittivity permeability compared to air (or other non-magnetic things).

However, in practice, some of the flux in each winding "leaks" out and isn't coupled to other windings. Also, there is always at least a little bit of current flowing in the primary that isn't coupled to the secondary, we call that the magnetizing current. That's why choice A says "essentially zero". For simple, first order analysis, you can ignore these effects. But often magnetics designers care a lot about them for esoteric reasons.

edit: Oops! Big mistake it's permeability, not permittivity, not at all the same thing, LOL.

 

[hidemi]

In a well designed (simple) transformer the magnetic core's job is to contain almost all of the flux and couple it into all of the windings. This works because it has very high permittivity compared to air (or other non-magnetic things).

However, in practice, some of the flux in each winding "leaks" out and isn't coupled to other windings. Also, there is always at least a little bit of current flowing in the primary that isn't coupled to the secondary, we call that the magnetizing current. That's why choice A says "essentially zero". For simple, first order analysis, you can ignore these effects. But often magnetics designers care a lot about them for esoteric reasons.

I got it. Thank you so much.