# Electronic – Transformer core radius and number of turns

transformer

I'm trying to solve this question.

For a specified input voltage and frequency, if the equivalent radius
of the core of a transformer is reduced by half, the factor by which
the number of turns in the primary should change to maintain the same
no load current I

If radius is halved, area becomes $$\ 1/4\$$ times. Hence to maintain the same no load current, there needs to be 4 times the number of turns we had earlier.

But the given answer is 2 times the number of turns. Why is that?

#### Best Answer

This answer assumes that "no load current" refers to the magnetization current in the primary of the transformer and that is defined by the magnetization inductance.

If the radius is halved then the inductance falls by 4 times because area is quartered. If the core is a regular shaped core with a decent value of permeability then you can assume that inductance is proportional to the square of turns hence, to restore the inductance, you need to double the turns to increase the inductance 4 times: -

Picture from here.

For a closed magnetic core $$\\ell\$$ becomes the mean length around the core.