EMF Equation of a Transformer

Consider a transformer arrangement as shown in figure.

N₁– Number of primary turns
N₂ – Number of secondary turns
Φ_m – Maximum value of flux in the core in wb
B_m – Maximum value of flux density in the core in wb/m²
A –  Area of the core in m²
f – Frequency of the AC supply in Hertz.
V₁ – Supply voltage across primary in volts
V₂ – Terminal voltage across secondary in volts
I₁ – Full load primary current in amperes
I₂ – Full load secondary current in amperes
E₁ – Emf induced in the primary in volts
E₂ – Emf induced in the secondary in volts

Since applied voltage is alternating in nature, the flux established is also an alternating one as shown in figure. From figure it is clear that the flux is attaining its maximum value in one quarter of the cycle i.e., T/E sec where ‘T’ is the time period in second.

We know that \mathrm{T}=\frac{1}{\mathrm{f}}, \quad where ‘f’ is the frequency in Hz.

∴ Average rate of change of flux =\frac{\phi_{\mathrm{m}}}{1 / 4 \mathrm{f}} \mathrm{wb} / \mathrm{seconds}

If we assume single turn coil, then according to Faradays laws of electromagnetic induction, the average value of emf induced / turn =4 \mathrm{f} \times \phi_{\mathrm{m}}

From factor =\frac{\text { R.M.S value }}{\text { Average value }}=1.11 (Since Φ_m is sinusoidal)

∴ RMS value = Factor × Average value

∴ RMS value of emf induced / turn = (1.11) × (4f × Φ_m) = 4.44 f Φ_m volts

∴ RMS value of emf induced in the entire primary winding

E₁ = 4.44 f Φ_m × N₁          or
E₁ = 4.44 f B_m AN₁ volts
Similarly RMS value of emf induced in the secondary E₂ =4.44 f Φ_m N₂ volts
or  E₁ = 4.44 f B_m A N₂ volts.