In a transformer, source of alternating current is applied to the primary winding. Due to this, the current in the primary winding (called as magnetizing current) produces alternating flux in the core of transformer. This alternating flux gets linked with the secondary winding, and because of the phenomenon of mutual induction an emf gets induced in the secondary winding. Magnitude of this induced emf can be found by using the following

N

N

Φ

f = frequency of the AC supply (in Hz)

As, shown in the fig., the flux rises sinusoidally to its maximum value Φ

Therefore,

average rate of change of flux =

Therefore,

average rate of change of flux = 4f Φ

Now,

Induced emf per turn = rate of change of flux per turn

Therefore, average emf per turn = 4f Φ

Now, we know, Form factor = RMS value / average value

Therefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn = 1.11 x 4f Φ

RMS value of induced emf in whole primary winding (E

E

Similarly, RMS induced emf in secondary winding (E

E

from the above equations 1 and 2,

This is called the

For an ideal transformer on no load, E

where, V

V

Where, K = constant

This constant K is known as

**EMF equation of the transformer**.### EMF equation of the Transformer

Let,N

_{1}= Number of turns in primary windingN

_{2}= Number of turns in secondary windingΦ

_{m}= Maximum flux in the core (in Wb) = (B_{m}x A)f = frequency of the AC supply (in Hz)

As, shown in the fig., the flux rises sinusoidally to its maximum value Φ

_{m}from 0. It reaches to the maximum value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).Therefore,

average rate of change of flux =

^{Φm}/_{(T/4)}=^{Φm}/_{(1/4f)}Therefore,

average rate of change of flux = 4f Φ

_{m}....... (Wb/s).Now,

Induced emf per turn = rate of change of flux per turn

Therefore, average emf per turn = 4f Φ

_{m}..........(Volts).Now, we know, Form factor = RMS value / average value

Therefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn = 1.11 x 4f Φ

_{m}= 4.44f Φ_{m}.RMS value of induced emf in whole primary winding (E

_{1}) = RMS value of emf per turn X Number of turns in primary windingE

_{1}= 4.44f N_{1}Φ_{m}............................. eq 1Similarly, RMS induced emf in secondary winding (E

_{2}) can be given asE

_{2}= 4.44f N_{2}Φ_{m}. ............................ eq 2from the above equations 1 and 2,

This is called the

**emf equation of transformer**, which shows, emf / number of turns is same for both primary and secondary winding.For an ideal transformer on no load, E

_{1}= V_{1}and E_{2}= V_{}_{2}.where, V

_{1}= supply voltage of primary windingV

_{2}= terminal voltage of secondary winding### Voltage Transformation Ratio (K)

As derived above,Where, K = constant

This constant K is known as

**voltage transformation ratio**.- If N
_{2}> N_{1}, i.e. K > 1, then the transformer is called step-up transformer. - If N
_{2}< N_{1}, i.e. K < 1, then the transformer is called step-down transformer.