# THE TRANSFORMER

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The transformer is a device which makes use of mutual induction to produce a large alternating current(AC) from asmall one, or a small alternating voltage from a large one. An ideal transformer consists of two coils, with different numbers of turns, wound on a soft iron core. These coils are electrically insulated from each other and from the core but they are magnetically l9inked through the core, i.e. flux is linked with both coils. The alternating voltage source, with emf Vp, is connected to the coil, known as primary with total number of turns Np. The resulting current Ip, through primary, gives rise to a varying magnetic flux in the iron core. If the flux changes at the rate of dpi/dt, the magnitude of the opposing emf is Np dpi/dt. If the resistance of the primary is assumed negligible small, the opposing emf is equal to the applied voltage, therefore

Vp = Np dpi/dt

The two coils are magnetically linked by the core, therefore the same changing magnetic flix dpi/dt passes the other coil, known as secondary with total number of turns Ns and induces an emf in it. The magnitude of the emf induced in the secondary is :-

Vs=Ns dpi/dt

Comparing with previous eqn.

ð  Vs/Ns=Vp/Np

ð  Which gives the relatipon between the applied alternating emf to the primary and transformed emf across the secondary in terms of numbers of turn in the two coils.

If Ns>Np, the transformer is called a step-up transformer it steps the voltageVp upto a higher voltage Vs.

If Ns<Np, then VsStep-Down transformer

When aload resistance is connected across the secondary, acurrent Is say, flows in the secondary coil.

Suppose that the current in the primary is Ip. If the ideal transformer is 100% efficient,

POWER:

Power Output=PowerInput

VsIs=VpIp

Or  Vs/Vp=Ip/Is=Np/Ns

EFFICIENCY:

The efficiency of a transformer is defined by

Efficiency = Poweroutput/Powerinput

The efficiencies of commercial transformer are very high-typically in the range 95-99%.

SYMBOL OF TRANSFORMER: 