### Working principle of transformer:

**The transformer is based on induction (mutual induction) principle****.**

From the above figure shows circuit diagram of transformer

Where,

**V _{1}= **Primary applied voltage

**E _{1}= **Primary (self) induced emf

**I _{1}= **Primary current

**N _{1}= **Primary number of turns

**V _{2}= **Secondary terminal voltage/Load voltage

**E _{2}= **Secondary induced emf

**I _{2 }= **Secondary current/Load current

**N _{2}= **Secondary number of turns

∅= Alternating flux

When alternating voltage (v_{1}) is applied to the primary winding a similar nature of current termed as exciting current flows through it. The exciting current produces an alternating flux (∅) in the core, which links with both the windings i.e primary and secondary.

According to * Faraday’s laws of electromagnetic induction*, there will be self-induced emf in the primary and mutually induced emf in the secondary winding. But according to

**primary induced emf will oppose the applied voltage that is why some time it is referred to as back emf. In magnitude the primary induced emf (E**

*Lenz’s law*_{1}) is almost equal to the applied voltage (V

_{1}). Therefore, we can say emf induced in the primary winding is equal and opposite of the applied voltage. i.e.

V_{1}=-E_{1}

When the load is connected across the secondary winding, the secondary emf (E_{2}) will cause a current (I_{2}) to flow through the load. Thus a transformer enables us to transfer a.c. power from one circuit to another i.e. primary to secondary winding through magnetic circuit by electromagnetic induction with a change in voltage level. This is the * working principle of the transformer*.

*Simple circuit for a 1-∅ transformer*

If

**E _{2}>E_{1}**, Step-up transformer

** E_{2}<E_{1},** Step-down transformer

V_{1}=E_{1}+ I_{1} (jX_{1}+R_{1})

E_{1}=-N_{1}

E_{2}=-N_{2}

The magnitudes of E_{2}&E_{1} depend upon the number of turns N2&N1 respectively. If N_{2 }>N_{1, }Then E_{2}>E_{1} and we get a step-up transformer. If N_{2 }<N_{1, }Then E_{2}<E_{1}, we get a step-down transformer.