Operating Principle of transformer:

1. As soon as the primary winding is connected to the single - phase AC supply, an alternating current starts flowing through it.
2. The ac primary current produces an alternating flux Ø in the core.
3. Most of this changing flux gets linked with the secondary winding through the core.
4. The varying flux will induce voltage into the secondary winding according to the Faraday’s Laws of electromagnetic induction.

Expression for EMF induced:

In a single phase transformer, the primary winding is connected across the AC supply. This forces an alternating current through the primary winding to produce an alternating flux (ø) in the core.

For deriving the EMF equation of a transformer refer to Fig. The primary winding is connected across the AC supply. This forces an alternating current through the primary winding to produce an alternating flux (ø) in the core.

This varying flux gets linked with the secondary and primary windings to induce the mutually induced and self-induced EMFs in the secondary and the primary winding respectively.

Induced Voltages:

1. Instantaneous flux ø:

As shown in Fig., the instantaneous flux changes in a sinusoidal manner with respect to time. Its frequency “f” is same as that of the AC voltage applied to the primary winding.

Ø=Øm  sinωt

 Where, ϕm = Maximum value of instantaneous flux.

ω = 2πf where “f” is the frequency of the flux waveform.

1. According to Faraday’s laws of electromagnetic induction, the induced EMF due to varying flux is given by,

$e=-N\dfrac{dØ}{dt}\ volts$

1. The value of induced EMF per turn can be obtained by substituting N = 1

$e\ =\ -\dfrac{dØ}{dt}$

Substituting $Ø=Ø_m\sin{\omega{}t}$

$e=-\dfrac{d}{dt}\left[Ø_m\sin{\omega{}t}\right]$

$e= - Ø_m\cos{\omega{}t}$

Maximum value of induced voltage per turn is given by substituting,cos ωt = ±1

$e_{max}=\omega{}Ø_m=2\pi{}fØ_m$

1. $e_{rms}\ per\ turn=\dfrac{e_{max}}{\sqrt{2}}=4.44fØ_m$
2. Let E1 be the rms induced voltage in primary winding with N1 turns and E2 be the rms induced voltage in secondary winding having N2 turns.

$E_1=Rms\ value\ of\ “e" \ per\ turn\times{}Number\ of\ primary\ turns$

$E_1=4.44fØ_m\times{}N_1\ volts$

     Similarly, rms value of induced voltage in the secondary winding is,

$E_1=Rms\ value\ of\ “e"\ per\ turn\times{}Number\ of\ secondary \ turns$

$E_1=4.44f\times{}N_2Ø_m\ volts$