Induced emf per in the one turn = Rate of change of flux per in the one turn
So, average emf per turn = 4f Φm ……….(Volts).
Since,Form factor = RMS value / Average value.
RMS value of emf per turn = Form factor X Average emf per turn.
The form factor of the sine wave is 1.11
Therefore, RMS value of emf per turn = 1.11 x 4f Φm = 4.44f Φm Volts.
The above equation for one turn.If there are N number of turns in the coil then emf equation of the transformer becomes,
E=4.44f N Φm Volts
f = frequency of the AC supply (in Hz).
Φm = Maximum flux in the core (in Webers) = (Bm x A)
N = Number of turns in the winding.[it can be primary or secondary]
Induced EMF Equation of Transformer In Primary, Secondary winding
RMS value of induced emf in the primary winding (Say E1) = RMS value of emf per turn X Number of turns in the primary winding
E1 = 4.44f N1 Φm ……………………….. (1)
Same as above, RMS induced emf in the secondary winding (Say E2) can be given as
E2 = 4.44f N2 Φm. ………………………. (2)
By dividing eqs (1) & (2).
The above relation between primary and secondary induced voltages is called the emf equation of transformer.We can observe emf/number of turns is same for both primary and secondary winding of a transformer.
Voltage Transformation Ratio (K) of Transformer
From equation (3) E1/N1=E2/N2=K
Where K = constant
This constant K is known as voltage transformation ratio.
If N2 > N1, i.e. K > 1, then the transformer is called step-up transformer.
If N2 < N1, i.e. K < 1, then the transformer is called step-down transformer
Based on the requirement we can use any transformer as step-up or step down by changing the supply.