Working of Transformer : - Technical Aspects

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 : -

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

In current post we will discuss technical aspects behind working of a transformer. A transformer may consists of two windings called primary and secondary windings. Primary winding is the winding that is connected to supply voltage and the secondary winding is the winding that is connected to load.

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. E₁ is termed as primary e.m.f. and e.m.f. E₂ is termed as secondary e.m.f. Clearly,
E₁=-N₁(dΦ/dt), and
E₂=-N₂(dΦ/dt)
Thus, E₂/E₁ = N₂/N₁
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. E₂ 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 V₁ 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. e₁ induced in the primary is given by,
e₁ = -N₁(dΦ/dt)
=> e₁ = - N₁ {d(Φ_m sin ωt)/dt}
=> e1 = -ωN₁Φ_mcos(ωt)
=> e1 = -2*π*f*N₁Φ_mcos(ωt)
=> e1 = -2*π*f*N₁Φ_msin(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*N₁*Φ_m => E₁ = E_m1/(2)^1/2
=> E_m1 = 4.44 f N₁Φ_m.