Consider a transformer arrangement as shown in figure.

**N _{1}**– Number of primary turns

**N**– Number of secondary turns

_{2}**Φ**– Maximum value of flux in the core in wb

_{m}**B**– Maximum value of flux density in the core in wb/m²

_{m}**A**– Area of the core in m²

**f**– Frequency of the AC supply in Hertz.

**V**– Supply voltage across primary in volts

_{1}**V**– Terminal voltage across secondary in volts

_{2}**I**– Full load primary current in amperes

_{1}**I**– Full load secondary current in amperes

_{2}**E**– Emf induced in the primary in volts

_{1}**E**– Emf induced in the secondary in volts

_{2}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

**E _{1}** = 4.44 f Φ

_{m}× N

_{1}or

**E**4.44 f B

_{1}=_{m}AN

_{1}volts

Similarly RMS value of emf induced in the secondary

**E**=4.44 f Φ

_{2}_{m}N

_{2}volts

or

**E**= 4.44 f B

_{1}_{m}A N

_{2}volts

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