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The flux in the core will be sinusoidally as shown below.

**EMF Equation of Transformer**

Let, N_{1}=Primary
number of turns

N_{2}
=Secondary number of turns

f =
Frequency of supply in Hz

The flux
in the core will be sinusoidally as shown below.

The flux
in the core increases from zero to Φ_{m} in one quarter cycle (1/4
second) Therefore, average rate of change of flux = Φ_{m}/(1/4f) = 4f Φ_{m}

Average
emf induced per turn = Average rate change of flux x 1 =4f Φ_{m} Volts

RMS value
of induced emf per turn = 1.11 x 4f Φ_{m} = 4.44f Φ_{m} Volts

RMS value
of induced emf in primary, E_{1} = 4.44f Φ_{m} N_{1}
Volts

RMS value
of induced emf in secondary, E_{2} = 4.44f Φ_{m} N_{2}
Volts

In an
ideal transformer on no load, V_{1} = E_{1}, V_{2} = E_{2}

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