Suppose , N1 = No. of turns of primary coil &
N2 = No. of turns of secondary coil of a transformer.
Φ_{m }= Maximum flux in core ( webers)
= B_{m } 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 Φ_{m } in one quarter of the cycle i.e in 1/4 f second
=4 f Φ_{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 = 4 f Φ_{m } 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 4fΦ_{m } = 4.44 fΦ_{m } volt
Now, r.m.s value of the induced e.m.f in the primary winding
∴ E_{1} = (induced e.m.f/turn) x No. of primary turns
∴ E_{1 }= 4.44 f Φ_{m } N1 (As Φ_{m } = B_{m} x A )
∴ E_{1} = 4.44 f N1B_{m }A .....................(i)
Similarly, r.m.s value of the e.m.f. induced in secondary is,
∴ E_{2 }= (induced e.m.f/turn) x No. of Secondary turns
= 4.44 f Φ_{m } N2 (As Φ_{m } = B_{m} x A )
⇒ E_{2} = 4.44 f N2 B_{m }A .....................(ii)
It is seen from equation (i) and (ii) that E_{1} / N1 = E_{2} / N2 = 4.44 f Φ_{m .}
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
∴ E_{1} / N1 = E_{2} / N2 = 4.44 f Φ_{m }= 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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