Transformer Equation Derivation

Transformer Equation Derivation: All About Transformer Formula

Let’s learn about transformer equation derivation in this article. The transformer is a static electronic device used to transfer the electrical power from one place to another by increasing and decreasing the voltage. There are many kinds of transformers that are invented for this purpose.

A Step-up transformer amplifies the voltage. Step down transformer decrease the voltage. Almost all transformers work with almost the same equation without the slightest change.

This blog will describe the whole of the transformers equation on this webpage. Please read it carefully and share your knowledge with others.

What Is Transformer Equation or Transformer Formula?

A transformer’s equation depends on the coil’s turn number, the current flow, and the voltage between the primary and secondary sides. The equation of the transformer is straightforward and given it below:

The transformer’s formula is, Np/Ns=Vp/Vs or Vs/Vp= Ip/Is or Np/Ns=Is/Ip

Here is the letter mean,

  • Np= Primary coil turns number
  • Ns= Secondary coil turns number
  • Vp= Primary voltage
  • Vs= Secondary voltage
  • Ip= Primary current
  • Is= Secondary current

EMF Equation Of Transformer

EMF stands for Electromotive force that is equal to the no current flows terminal potential difference. In a transformer, EMF depends on the number of turns in both coils, induced flux in the transformer’s magnetic core, and the AC supply frequency.

EMF equation of a transformer is Ep/Np=Es/Ns=4.44fΦm.


  • Np = Turns in the primary coil.
  • Ns = Turns in the secondary coil.
  • Φm = Induced flux in the magnetic core (in Wb) = (Bm x A)
  • f = Supply frequency (in Hz)

change of flux = Φm /(T/4) = Φm /(1/4f)

Average rate of change of flux = 4f Φm(Wb/s).

Φ varies sinusoidally, the form factor of a sine wave is 1.11

RMS value of EMF per turn = 1.11 x 4f Φm = 4.44f Φm…

Transformer Equation Example

Examples can help to recognize the application of the equation. Now some examples are given for the reader’s purposes.

Transformer Equation Example

Example 1 (Step-down): A transformer’s primary voltage is 750, and the secondary voltage is 220. Primary windings are 1600. Calculate the secondary windings.

Solution: According to the transformers equation, here is Np= 1600, Vp= 750, Vs= 220, Ns=?

Np/Ns= Vp/Vs

Ns= (Np*Vs)/ Vp= (1600*220)/ 750= 469

The answer of the secondary windings are 469.

Example 2 (Step-up): If a transformer’s primary current is 50A and the primary voltage is 220. The secondary voltage is 600. Calculate the secondary current.

Solution: According to the transformers equation, here is Ip= 50, Vp= 220, Vs= 600, Is=?

We know, Vp/Vs=Is/Ip

Is= (Vp*Ip)/Vs= (220*50)/600= 18

The answer of the secondary current is 18 ampere.

Example 3 (Step-up): If a transformer’s primary current is 15A and the primary windings are 1000. The secondary current is 5A. Calculate the secondary windings.

Solution: According to the transformers equation, here is Ip= 15, Np= 1000, Is= 5, Ns=?

We know, Np/Ns=Is/Ip

Ns= (Np*Ip)/Is= (1000*15)/5= 3000

The answer of the secondary windings are 3000.

By the transformer’s law, you can calculate the primary voltage, secondary voltage, primary current, secondary current, primary coil turns number, or the secondary coil turns number. Just implement these values on the equation which is given on this question and get your result.


About the Author: Mehedi Hasan

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