E.M.F. EQUATION OF A TRANSFORMER

Let N₁ =No. of turns in primary

N₂ =No. of turns in secondary

φ_m =Maximum flux in core in Webbers = Bm × A

f =frequency of a.c. input in HZ

flux increases from its zero value to maximum value φ_m in one quarter of the cycle i.e. in 1/4f second.

Average rate of change of flux = φ_m / (1 / 4f) = 4fφ_m Wb/s or volt

Now, rate of change of flux per turn means induced e.m.f. in volts.

Average e.m.f. / turn = 4fφ_m volt

In an ideal transformer on no load,

V₁ = E₁ and E₂ = V₂

Where V₂ is the terminal voltage.

VOLTAGE TRANSFORMATION RATIO (K)

E₂/E₁=N₂/N₁=K

This constant K is known as voltage transformation ratio.

If N₂>N₁ i.e. K>1, then transformer is called step-up transformer.

If N₂₁ i.e. K<1, style="mso-bidi-font-weight:normal">step-down transformer.

Again for an ideal transformer,

Input VA=Output VA

V₁I₁=V₂I₂ or I₂/I₁=V₁/V₂=1/K

Hence, currents are in the inverse ratio of the voltage transformation ratio.