In this article we will discuss technical aspects of working of transformer and will drive emf equation of the transformer.

Hello Friends,

In one of my previous post Basics of Transformer, We have discussed some basics and simple working of transformer. A quick revision is here : -### Working of Transformer : -

As I said a transformer has two windings viz. Primary and secondary winding. When we apply an alternating voltage say V1 to the primary winding of the transformer, an alternating flux ¤(fi) is set up in the core. This alternating flux links both the windings and induces e.m.f.s E1 and E2 in them according to Faraday's law of electromagnetic induction. The e.m.f. E_{1} is termed as primary e.m.f. and e.m.f. E_{2} is termed as secondary e.m.f. Clearly,

E_{1}=-N_{1}(dΦ/dt), and

E_{2}=-N_{2}(dΦ/dt)

Thus, E_{2}/E_{1} = N_{2}/N_{1}

Here one thing should be noted that the magnitude of induced voltages depends upon number of turns in both windings. Hence if number of turns in primary are more than that in secondary more voltage will be induced in primary and transformer will be step down kind and if number of secondary is more secondary e.m.f. E_{2} will be more and transformer will be said to step up transformer. You can understand working of transformer with the help of following video :

### E.M.F. Equation of a transformer : -

E.M.F. Equation of any electrical appliance is very important, thus it is also of prime importance for a transformer. Consider that an alternating voltage V_{1} of frequency f is applied to the primary of a transformer. Due to this alternating voltage, alternating flux Φ produced by the primary can be represented as :
Φ = Φ_{m} sin ωt

The instantaneous e.m.f. e_{1} induced in the primary is given by,

e_{1} = -N_{1}(dΦ/dt)

=> e_{1} = - N_{1} {d(Φ_{m} sin ωt)/dt}

=> e1 = -ωN_{1}Φ_{m}cos(ωt)

=> e1 = -2*π*f*N_{1}Φ_{m}cos(ωt)

=> e1 = -2*π*f*N_{1}Φ_{m}sin(ωt-90)

It is clear from the above equation that maximum value of induced e.m.f. in the primary is

E_{m1} = 2*π*f*N_{1}*Φ_{m} => E_{1} = E_{m1}/(2)^{1/2}

=> E_{m1} = 4.44 f N_{1}Φ_{m}.

In one of my previous post Basics of Transformer, We have discussed some basics and simple working of transformer. A quick revision is here : -

- Static Device - No rotating part.
- Can raise or drop voltage level.
- Winding and Core are essential parts with a.c. Supply.

E

E

Thus, E

Here one thing should be noted that the magnitude of induced voltages depends upon number of turns in both windings. Hence if number of turns in primary are more than that in secondary more voltage will be induced in primary and transformer will be step down kind and if number of secondary is more secondary e.m.f. E

The instantaneous e.m.f. e

e

=> e

=> e1 = -ωN

=> e1 = -2*π*f*N

=> e1 = -2*π*f*N

It is clear from the above equation that maximum value of induced e.m.f. in the primary is

E

=> E

Article Was Last Updated on **Monday, March 12th, 2018 At 01:11:54 am**

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