**EMF equation of transformer** is very important for understanding the working of the transformer.When sinusoidal voltage is applied to primary of the transformer it draws magnetizing current to set up flux in the core. The flux links to the secondary and produce EMF. We can easily derive the EMF equation of transformer by calculating the rate of change of the flux in one cycle of AC waveform. Induced EMF in the primary and secondary of the transformer also depends on the turns ratio of transformer. The ratio of secondary EMF to primary EMF is called voltage transformation ratio of the transformer. The ratio of Primary turns to secondary turns is called **transformer turns ratio**(TTR).

The flux set up in the core gets linked to the primary and secondary winding of the transformer. The alternating flux set up in the core when links to turns of the primary and secondary winding induces voltage called EMF. The EMF induced in the transformer winding depends on number of turns and rate of change of the flux. The EMF induced across the primary and secondary always opposes the applied voltage.

According to Faraday’s law of electromagnetic induction, if the alternating flux links to a coil the voltage is induced in the coil. The voltage induced in the primary and the secondary winding of the transformer is as given below. The RMS value of secondary induced EMF and primary induced EMF can be calculated using Faraday’s law of electromagnetic induction.

**Derivation of EMF Equation Of Transformer **

**Ep = – Np x dФ/dt ———(1)**

**Ф = Фm Sinwt ————-(2)**

**Ep = – Np x wФm**

**Ep(max) = Np 2πfФm ———–(3)**

**Ep(RMS) = Ep(Max)/√2 ——-(4)**

**Ep(RMS) = 4.44 Np fФm ——-(5)**

**Es(RMS) = 4.44 Ns fФm ——-(6)**

**The general EMF Equation of the transformer is;**

**E= 4.44 N fФm ———–(7)**

**Voltage Transformation Ratio of Transformer**

The ratio of the secondary turns to primary turns is known as the voltage transformation ratio of the transformer and it is denoted by letter ‘K’.

**ES/Ep = Ns/Np =K ——–(7)**

If the voltage transformation ratio (K) is less than 1, the transformer is called step down transformer.

The magnetizing MMF is negligible when substantial current flows in the primary and secondary winding of the transformer. The total MMF of the primary and secondary MMF is equal to the magnetizing MMF. The transformer is a constant flux machine as long as voltage and frequency remains constant.

MMF_{primary} + MMF_{secondary} = MMF_{magnetizing}

When transformer is substantially loaded, the magnetizing MMF can be neglected.

MMF_{primary} + MMF_{secondary} = 0

Np x Ip + Ns x Is =0

Np x Ip = -Ns x Is

**Ip/Is = – Ns/Np ——(8)**

Es / Ep = Ip / Is = K

**Es / Ep = Ns / Np =Ip / Is = K**

**The voltage transformation ratio equation (7) of transformer is true** if the flux in the transformer core is constant. The flux in the transformer changes if the supply voltage and or frequency gets deviate from its designed value.

**Transformer Turns Ratio**

The ratio of primary(Np) to secondary turns(Ns) of the transformer is known as transformer turns ratio,or TTR. It is denoted by letter ‘a’.

**
**Np / Ns = a

Ns / Np = K

Np / Ns = 1/K

a = 1 / K

**
**Es / Ep = Ns / Np =Ip / Is = K

Ep / ES = Np/ Ns = Is / Ip = 1/K

**Ep / Es = Np / Ns = Is / Ip = a**

**Solved Problems on transformer EMF equation**

*A two-winding transformer has primary winding with 300 turns and secondary winding with 10 turns. The primary winding is connected to 3300 V supply system. Calculate-*

**Secondary voltage at no load****Primary current when the 100-amp load connected to secondary****Apparent power flowing in the primary and secondary circuit****Turns ratio and voltage transformation ratio of transformer?**

**First transformer law:**

**Es = 110 Volts**

**Second transformer law:**

**Ip = 3.33 Amps.**

**Apparent power in primary circuit = Ep x Ip**

**= 10989 VA**

**Apparent power in secondary circuit = Es x Is**

**= 11000 VA**

**Transformer turns ratio(TTR)**

**a = Np/Ns**

a = 300/10

**a = 30**

**Transformer voltage transformation ratio**

**K = Es/ Ep**

**K = 0.0333**

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