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.

Similar Reads

What is a Transformer?

A transformer is a static electrical device that transmits AC power from one circuit to another at a constant frequency, but the voltage level may be changed, implying the voltage can be increased or decreased depending on the requirement....

Types of Transformer

Transformer types based on Voltage Level...

Working Principle of a Transformer

The fundamental principle of how the transformer functions are mutual induction between the two coils or Faraday’s Law of Electromagnetic Induction. Below is a description of how the transformer operates. The laminated silicon steel core of the transformer is covered by two distinct windings. According to the diagram below, the primary winding is the one to which the AC supply is connected, and the secondary winding is the one to which the load is connected. Only alternating current can be used because mutual induction between the two windings requires an alternating flux....

Parts of a Transformer

A transformer majorly consists of three parts:...

Ideal Transformer

An ideal transformer is a purely theoretical transformer that has no losses at all, including no core losses, copper losses, or other transformer losses. This transformer is thought to be 100% efficient....

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....

Turn Ratio

Turn Ratio is a measure to determine whether the secondary coil of a transformer has more or lesser windings than the primary. The number of windings on a primary coil is equal to “Np,” while the number of windings on a secondary coil is “Ns,” representing the number of turns....

Efficiency of Transformer

The efficiency of a transformer is also known as commercial efficiency. It is represented by the letter ‘η’. The efficiency of a Transformer is described as the ratio of output (in W or kW) to input (in W or kW)....

Energy Losses in a Transformer

We used an ideal transformer in the previous equations (without any energy losses). However, some energy losses do occur in actual transformer for the following reasons:...

Application of Transformer

The following are some of the most common uses for transformer:...

Solved Examples on Transformer

Example 1: A transformer primary winding is powered by a 120 V ac source. If the turn ratio is 10, what does the secondary voltage equal?...

FAQs on Transformer

Question 1: What is Transformer?...