EMF Equation Of the Transformer
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.
Transformer EMF Equation
Now lets know how to find the magnitude of the inducted EMF in a transformer by EMF equation of the transformer.
N1 = Number of turns in primary windings.
N2 = Number of turns in second windings.
Φm = Maximum flux in the core in Webbers.
- Φm= Bm.A,
f = Frequency of A.C input in Hz.
Click image to enlarge
As shown in fig above- flux increases from its zero value to maximum value Φm in one quarter of the cycle i.e. in ¼ second.
Average rate of change of flux = [ Φm / (¼ f.)]
= 4f Φm 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 Φm volt.
If flux Φm 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 Φm= 4.44f Φm 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 Φm ……….. (i)
E1 = 4.44 x f N1 Bm A … [as (Φm= BmA)]
Similarly, r.m.s value of the e.m.f. induced in secondary is,
E2 = 4.44 x f N2 Φm ……….. (ii)
E2 = 4.44 x f N2 Bm A. … [as (Φm= BmA)]
It’s seen from (i) and (ii) that: EMF Equation of the Transformer =
E1 / N1= E2 / N2 = 4.44 x f Φm. …… (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.
V1 = E1
E2 = V2
- 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
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.
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.
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