Let,

N

_{1}= No. of turns in primary Winding
N

_{2}= No. of turns in secondary Winding
Φ

_{m}= Maximum flux in core in webers
= B

_{m}x A
F = Frequency of AC input in Hz.

In the fig. flux rises from its value zero to maximum Φ

_{m }value in one quarter of the cycle i.e. in 1/4 f second.
∴ Average rate of change of flux = Φm /1/4f

= 4 Wb/s or volt

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

If flux Φ varies sinusoidally, then r.m.s. value of induced e.m.f. is obtained by multiplying the average value with form factor.

Form factor = r.m.s. value / average value =1.11

∴ r.m.s. value of e.m.f./turn = 1.11 × 4 f Φ

_{m}
= 4.44 f Φ

_{m}volt.
Now, r.m.s. value of the induced e.m.f. in the whole of primary winding

= (induced e.m.f/turn) × No. of primary turns

E1 = 4.44fN

_{1}Φ_{m}= 4.44fN_{1}B_{m}A ---->1
Similarly, r.m.s. value of the e.m.f. induced in secondary is,

E2 = 4.44fN2 Φ

_{m}= 4.44fN_{2}B_{m}A ---->2
From the equation 1 ----> 2 that E

_{1}/N_{1}= E_{2}/N_{2}= 4.44f Φ_{m}.
It means that e.m.f./turn is the same in both the primary and secondary windings.

In an ideal transformer on no-load, V

_{1}=E_{1}and E_{2}=V_{2}. Where V_{2}is the terminal voltage
I also write article on the same topic. Pl check and let me know if it is OK. Your expert comments pls.

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