Inrush Current Limiter Circuit

So, why isn't the inrush current simply the applied voltage divided by the resistance of the winding, before the magnetic field has started to build up?

Because it's necessary to account for any residual (remnant) magnetism in the core and the core's characteristics. As you can see the stuff in parenthesis † can result in a significant multiplier to your approach (the stuff to the left of the parentheses).

Although we don't normally think of it as such, the core is an energy storage device, and it takes a lot of energy to instantaneously switch its state so that all the magnetic domains line up with the newly applied voltage/current. That's one of the reasons why we see statements like "...the inrush current can be 4-12 times full load current...).

Hit a transformer which was switched off with the core fully "charged" and you may get the top of the range depending upon where on the voltage waveform the switch was closed. Of course it's all statistical as to when the switch is opened then closed so we provide a range of values.

You may find your answer in this paper:

http://pulsedmagnets.web.psi.ch/Air-core%20transformer.pdf

Plenty on the topic by Googling.

Thanks for your reply,

The link refers the air core inductance simply the coil alone, but not the calculation for toroidal transformer air core inductance.

In torodial transformers the winding goes from top to bottom and not in circle.

for inrush current calculation we need to account air core inductance?

Waiting for your valuable answer.

Best regards,

M.R.T

The design of the toroidal transformer results in very low air core inductance. But then inrush current can be very high. It may come up to 60x load current.

Best way to reduce the inrush is to implement a premagnetising procedure.