What is a transformer? Explain the principle, construction, working and theory of a transformer.
Hint: You might begin by explaining what a transformer is. After that, you can discuss the underlying principle that governs how transformers work. Then describe the basic setup of a transformer. Then finally write how a transformer works.
An electrical device that can change the A.C. current is known as a transformer.
Principle –
A transformer operates based on the concept of mutual induction. Mutual induction refers to the phenomenon where a change in the magnetic flux associated with a coil induces an E.M.F. is induced in the neighboring coil.
Construction –
A transformer consists of a rectangular iron core. Two coils, a primary (P) coil with two sides P1 and P2, and a secondary (S) coil with two sides S1 and S2. Both these coils are insulated from the Ferro-magnetic iron core. The source of alternating current is linked to the primary winding, while the output is taken from the secondary winding, which is connected in parallel to a resistor R.
Working –
For an ideal transformer, we assume that the resistances of the primary and secondary coils are minimal.
Let the E.M.F. of the alternating current provided by the A.C. source be
EP = E O sinωt
Let’s assume that the primary winding to be a pure inductance, so here IP will lag behind the voltage EP by 90º. Thus the power factor for primary coil becomes, \(cosϕ=cos90^{\circ } = 0\).
Let that the number of turns in primary wire be EP and secondary wire be Ns
According to faraday law, the induced E.M.F.
The flux through a single turn of both coils will be identical.
Let the flux through one turn be denoted as ϕ, the flux through the primary coil as ϕP, and the flux through the secondary coil as ϕS.
So ϕP = NP ϕ
ϕS = NS ϕ
We also know by Faraday’s law
\(E=\frac{dϕ}{dt}\)So for the primary coil this equation becomes
\(ES=\frac{dϕ_S}{dt}\)….. (Equation 1)
And for the secondary coil this equation becomes
\(E_P=\frac{dϕ_P}{dt}\)…..(Equation 2)
Dividing equation 1 by equation 2
\(\frac{E_S}{E_P}=\frac{dϕ_S}{dϕ_P}=\frac{N_Sϕ}{N_Pϕ}\)\(E_S=E_p\frac{N_S}{N_p}\)…(Equation 3)
We know that
P=V I
Here
P=Power
V=Voltage
I=Current
For primary coil this equation becomes
\(P_P=E_PI_P\)(Equation 4)
For secondary coil this equation becomes
\(P_S=E_SI_S\)(Equation 5)
In an ideal transformer, no energy is wasted, therefore
\(P_P = P_S\)\( E_PI_P=E_SI_S\)
\(I_S=I_PE_PE_S\)
\(I_S=I_P\frac{E_P}{E_S} \)\((∵\frac{E_P}{E_S}=\frac{N_P}{N_S})\)
\(I_S=I_P\frac{N_P}{N_S}\)
Note – A transformer that increases the A.C. voltage is known as a step up transformer \((N_S>N_P) \)and the transformer that decreases the A.C. voltage is known as a step down transformer\((N_S<N_P)\) . Moreover, an iron core is employed because it is a ferromagnetic material that enhances the strength of the magnetic field.
