EMF Equation of Ideal Transformer
Let Np is the main winding’s number of turns, whereas Ns is the secondary winding’s number of turns. When an AC voltage is given to the transformer main coil, the current generated creates an alternating magnetic flux that connects the secondary coil and generates an emf. The number of turns in the secondary coil determines the value of this emf. Consider an ideal (lossless) transformer with zero primary coil resistance (no voltage drop across coil) and all flux in the core connecting both primary and secondary windings. When the voltage Vp is delivered to the primary coil, let be the flux linkage in each turn in the core at time t owing to the current in the primary coil.
The induced emf or voltage (εs) in the secondary with Ns turns is then calculated.
εs = –Ns x dϕ/dt ……(1)
In addition, the alternating flux generates a reverse emf in the main. This is it.
εp = –Np x dϕ/dt ……(2)
And for an ideal transformer, εp=Vp
By approximation, if the secondary is an open circuit or the current drawn from it is modest, εs=Vs.
The voltage across the secondary coil is Vs. As a result, Equations (1) and (2) may be written as
Vs = –Ns x dϕ/dt ……(3)
Vp = –Np x dϕ/dt ……(4)
From Equations (3) and (4), we have
Vs / Vp = Ns / Np ……(5)
The above equation is known as Transformer Equation or Transformer Formula.
The following three assumptions are used to get the previous relationship:
- The primary and secondary coils’ electrical resistances are insignificant.
- The flux connectivity to both the primary and secondary coils is the same, or very few fluxes escape from the core.
- The secondary current is insignificant.
Transformer
Transformer is the simplest device that is used to transfer electrical energy from one alternating-current circuit to another circuit or multiple circuits, through the process of electromagnetic induction. A transformer works on the principle of electromagnetic induction to step up or step down voltage. Transformer either increases AC voltage (Step-up transformer) or decreases AC voltage (Step-down transformer). Transformer which is normally utilized in the transmission and distribution of alternating current power is fundamentally a voltage control device. Transformer are used for a wide range of purposes, including increasing the voltage from electric generators to enable long-distance transmission of electricity and decreasing the voltage of conventional power circuits to run low-voltage devices like doorbells and toy electric trains.