Suppose , N1 = No. of turns of primary coil &
N2 = No. of turns of secondary coil of a transformer.
Φm = Maximum flux in core ( webers)
= Bm x A
f= frequency of alternating current in Hz
From the figure , it has been seen that the flux Φ increases from its zero value to maximum value Φm in one quarter of the cycle i.e in 1/4 f second
=4 f Φm Wb/s or volt
Now, rate of change of flux per turn means induced e.m.f in volts.
∴ average e.m.f/ turn = 4 f Φm volt
If the magnitude of flux Φ varies sinusoidally, then the r.m.s value of induced e.m.f is obtained by multiplying the average value with from factor.
∴ r.m.s value of e.m.f./turn = 1.11 x 4fΦm = 4.44 fΦm volt
Now, r.m.s value of the induced e.m.f in the primary winding
∴ E1 = (induced e.m.f/turn) x No. of primary turns
∴ E1 = 4.44 f Φm N1 (As Φm = Bm x A )
∴ E1 = 4.44 f N1Bm A .....................(i)
Similarly, r.m.s value of the e.m.f. induced in secondary is,
∴ E2 = (induced e.m.f/turn) x No. of Secondary turns
= 4.44 f Φm N2 (As Φm = Bm x A )
⇒ E2 = 4.44 f N2 Bm A .....................(ii)
It is seen from equation (i) and (ii) that E1 / N1 = E2 / N2 = 4.44 f Φm .
from the above equation it is seen that the e.m.f/ turn is the same in both primary and secondary windings.
Voltage Transformation Ratio :-
From equation (i) and (ii) ,we get
∴ E1 / N1 = E2 / N2 = 4.44 f Φm = K
Constant K is known as voltage transformation ratio.
i) If N2 > N1 i.e K > 1,then transformer is called step-up transformer.
ii) If N2 < N1 i.e K < 1,then transformer is called step-down transformer.
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