EMF Equation Of a Transformer

EMF Equation Of the Transformer

Introduction

Magnitude of the induced EMF (or Voltage) in a transformer can be found by EMF equation of the transformer. When a source of alternating current (AC) is applied to the primary winding of the transformer which is known as magnetizing current, it produces alternating flux in the core of a transformer.

The produced alternating flux  in the primary of the transformer gets linked with the secondary winding of the transformer by mutual induction as it is alternating flux in nature, there must be a rate of change of flux according to Faraday’s law of electromagnetic induction which states that if a conductor or coil links with any changing flux, there must be an induced emf in it.

The same happens in transformer as well as induction motor as induction motor is fundamentally a transformer.

• Also read: Power Transformers Maintenance, Diagnostic & Monitoring

Transformer EMF Equation

Now lets know how to find the magnitude of the inducted EMF in a transformer by EMF equation of the transformer.

Lets,

N₁ = Number of turns in primary windings.    

N₂ = Number of turns in second windings.

Φ_m = Maximum flux in the core in Webbers.                                                   

• Φ_m= B_m.A,

f = Frequency of A.C input in H_z.

• Also Read: EMF equation of an Alternator or AC generator

Click image to enlarge

As shown in fig above- flux increases from its zero value to maximum value Φ_m  in one quarter of the cycle i.e. in ¼ second.

Average rate of change of flux = [ Φ_{m /} (¼ f.)]

= 4f Φ_m Wb/s or volt

Now rate of change of flux per turn means induced e.m.f in volts.

Average e.m.f /per turn = 4f Φ_m volt.

If flux Φ_m varies sinusoidally, then r.m.s value of induced .e.m.f is obtained by multiplying the average value with form factor.

Form factor = r.m.s value / Average value = 1.11

r.m.s value of e.m.f/turn = 1.11. 4f Φ_m= 4.44f Φ_m volt

now r.m.s value of the induced e.m.f in the whole primary winding.

= ( induced e.m.f/turn) x number of primary turns

E₁ = 4.44 x f x N₁ Φ_{m ……….. (i)}

E₁ = 4.44 x f N₁ B_m A … [as  (Φ_m= B_mA)]

Similarly, r.m.s value of the e.m.f. induced in secondary is,

E₂ = 4.44 x f N₂ Φ_{m ……….. (ii)}

E₂ = 4.44 x f N₂ B_m A.  … [as  (Φ_m= B_mA)]

It’s seen from (i) and (ii) that: EMF Equation of the Transformer =

E₁ / N₁= E₂ / N₂ = 4.44 x f Φ_{m.  …… (iii)}

 It means that e.m.f / turn is the same  in both the primary and secondary windings in the transformer like flux in Primary and Secondary Winding of the Transformer is same.

Moreover, we already know that from the power equation of the transformer, i.e, in ideal Transformer (there are no losses in transformer) on no-load,

V₁ = E₁

and

E₂ = V₂

Where,

• V₁ = supply voltage of primary winding
• E₂ = terminal voltage induced in the secondary winding of the transformer.

You may also read: Transformers Fire Protection System – Causes, Types & Requirements

Voltage Transformation Ratio (K)

As we have derived from the above EMF equation of the transformer _(iii);

E₁ / N₁= E₂ / N₂ = K

Where,

K = Constant

The constant “K” is known as voltage transformation ratio.

• If N₂ > N₁, i.e. K > 1, then the transformer is called step-up transformer.
• If N₂ < N₁, i.e. K < 1, then the transformer is called step-down transformer.

Where,

N₁ = Primary number of turns of the coil in a transformer.

N₂ = Secondary number of turns.

• You may also read: Current Transformers (CT) – Types, Characteristic & Applications

Power Equation of the Transformer

We have already discussed it in our previous post which can be seen it here.

You may also read:

• Transformer Efficiency, All day Efficiency & Condition for Maximum Efficiency
• Can we operate a 60HZ Transformer on 50Hz Supply Source and Vice Versa?
• How to Calculate the Rating of Transformer in kVA (1 Phase and 3 Phase)?