# Describe the Basic Principle of Operation of a Single Phase Transformer and Derive the Emf Equation. - Basic Electrical and Electronics Engineering

Sum

Describe the basic principle of operation of a single phase transformer and derive the emf equation.

#### Solution

When an alternating voltage π1 is applied to a primary winding, an alternating current πΌ1flows in it producing an alternating flux in the core. As per Faraday’s laws of electromagnetic induction, an emf π1 is induced in the primary winding.

e_1=-N_1(dvarphi)/(dt)

Where π1 is the number of turns in the primary winding. The induced emf in the primary winding is nearly equal and opposite to the applied voltage π1.
Assuming leakage flux to be negligible, almost the flux produced in primary winding links with the secondary winding. Hence, an emf π2 is induced in the secondary winding.

e_2=-N_2(dvarphi)/(dt)

Where π2 is the number of turns in the secondary winding. If the secondary circuit is closed through the load, a current πΌ2 flows in he secondary winding. Thus energy is transferred from the primary winding to the secondary winding.

EMF EQUATION.

As the primary winding is excited by a sinusoidal alternating voltage, an alternating current flows in the winding producing a sinusoidally varying flux π in the core.

π=πππ ππππ‘

As per Faraday’s law of electromagnetic induction an emf π1 is induced in the primary winding.

e_1=-N_1(dvarphi)/(dt)

e_1=-N_1(dvarphi)/(dt)(πππ ππππ‘)

π1=−π1ππππππ ππ‘ = −π1πππsin (ππ‘−90°) = 2πππ1πππsin (ππ‘−90°)
Maximum value of induced emf = 2πππππ1
Hence, rms value of induced emf in primary winding is given by,

E_1=(E_(max))/sqrt2=(2pifN_1varphi_m)/sqrt2=4.44 fN_1varphi_m

Similarly rms value of induced emf in the secondary winding is given by,

πΈ2=4.44ππ2ππ

Also, E_1/N_1=E_2/N_2=4.44fvarphim

Thus emf per turn is same in primary and secondary winding and an equal emf is induced in each turn of the primary and secondary winding.

Concept: Working Principle of Single Phase Transformer
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2018-2019 (December) CBCGS

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