## What is a Transformer? | Working Principle | EMF Equation

### What is a Transformer?

A transformer may be defined as a static electrical device that transfers electrical energy from one circuit to another circuit at the same frequency but with changed voltage (or current or both) through a magnetic circuit.

### Working Principle of Transformer

When alternating voltage V1 is applied to the primary winding of a transformer a current (termed as exciting current, IΦ) flows through it. The exciting current produces an alternating flux (Φ) in the core, which links with both the winding (primary and secondary). According to Faraday's laws of electromagnetic induction, the flux will cause self-induced emf E1 in the primary and mutually induced emf E2 in the secondary winding. But according to Lenz's law primary induced emf will oppose the applied voltage and in magnitude, this primary induced emf is (almost) equal to the applied voltage. Therefore, in brief, we can say emf induced in the primary winding is equal and opposite to the applied voltage.

When a load is connected on the secondary side, the current will start flowing in the secondary winding. The voltage induced in the secondary winding is responsible to deliver power to the load connected to it. In this way, power is transferred from one circuit (primary) to another (secondary) winding through a magnetic circuit by electromagnetic induction. This is the working principle of the transformer. The induced emf in the secondary E2 is also in phase opposition to the applied voltage V1 at primary. if the secondary is open-circuited, terminal voltage V2 at the secondary is equal in magnitude and in phase with the induced emf at secondary.

### EMF Equation of Transformer

Since the applied voltage is sinusoidal at the primary, the flux produced by the exciting current is also sinusoidal.

If N1 be the primary number of turns, then the RMS values of induced voltage at primary is given by-

E1 = 4.44 Φmax f N1

(As the induced voltage in the primary winding is equal and opposite to the applied voltage, so V1 = 4.44 Φmax f N1 ).

Similarly, the RMS value of the induced emf at secondary is obtained as

E2 = 4.44 Φmaxf N2

Thus for a single-phase ideal transformer, the expressions for the induced voltages at the primary as well as at the secondary windings can be obtained from above Eqns.

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