# If the supply frequency of a transformer increases, the secondary output voltage of the transformer

If the supply frequency of a transformer increases, the secondary output voltage of the transformer

#### SOLUTION

If the supply frequency of a transformer increases, the secondary output voltage of the transformer increase.

The EMF Equation Of A Transformer is given by

$E = 4.44fBNA$

where

E = the voltage in the winding either primary or secondary,
f = frequency
B = flux density in the core
N = Number of turns on the winding
A = Cross area of the core

A transformer is designed for some constant parameters like frequency. So if the frequency increases, the secondary voltage or emf increases. But with high frequency, there is an increase in transformer losses like core loss and conductor skin effect. Also with high frequency, the magnetizing current becomes low and with low frequency the magnetizing current becomes high.

The higher the input frequency, the higher will be the rate of change of magnetic flux, which results in higher induced EMF

Frequency ~ Rate of Change of Magnetic Flux ~ Induced EMF

Note:-  There are some other conditions which should be kept in mind

Condition 1:- If you are maintaining the same voltage but higher frequency, flux ( V/f ) in the transformer falls, the induced emf would hence remain the same and would not increase. Although the rate of change of flux increases due to increased frequency but the value of flux is reduced and hence the overall effect is that voltage induced in the secondary remains the same but at a higher frequency of course.

Condition 2:- If you are increasing primary voltage along with increasing frequency so as to maintain constant flux, only in that case the secondary voltage will increase. Therefore you can safely conclude that secondary voltage depends only upon the primary voltage and turns ratio.

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