EMF equation of Transformers:
A transformer is a static device which has two windings,, one is primary winding and other is secondary winding.When an alternating current is applied to primary an alternating flux is developed ,which links with secondary windings and an emf is induced in the secondary windings according to mutual induction.This magnitude of induced emf can be found using the below emf equation of transformer.
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| E.M.F equation of a transformer |
Let N1 = number of turns in primary windings
N2 = number of turns in secondary windings
Φm= Maximum flux in core in webers
= BA
f = frequency of a.c. input in Hz
As shown in the above figure of EMF equation of transformer, flux increases from its zero value to maximum value Φm in one quarter of cycle i.e. 1/4f second .
Average rate of change flux = Φm/(1/4f)
= 4fΦm
Rate of change of flux per turn means induced e.m.f in volts.
Average e.m.f/turn = 4fΦmvolt
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
Now r.m.s value of induced e.m.f in whole of primary = (induced e.m.f/turn)x number of primary turns
E1 = 4.44fN1Φm
E1 = 4.44fN1BA
Similarly, r.m.s value of the induced emf in secondary of transformer is
E2 = 4.44fN2BA
It can be observed from above equations that
E1/N1 = E2/N2 = 4.44fΦm
This is the emf equation of transformer, which means that e.m.f/turn is the same in both the primary and secondary windings.
For an ideal transformer on no load, E1 = V1 and E2 = V2 .
where V1 = supply voltage of the primary winding
V2 = terminal voltage of secondary winding
Voltage Transformation Ratio(K):
From equations above we get
E2/E1 = N2/N1 =k
the constant 'K' is called voltage transformation ratio .
1. If N2>N1 i.e. K>1, then transformer is called Step up transformer .
2. If N2<N1 i.e. K<1, then transformer is called Step down transformer .