Transformers, Equation of transformer in physics

Definition of Transformers

Transformers

Transformers are devices use for changing the voltages or currents of an A.C supply. The transformers may be used to increase or decrease the A.C (alternating current) supply. The transformers make use of the properties of mutual inductance to change the voltage of the alternating current (A.C) supply.

Transformer may be used in homes to give a low voltage output from the main for our electronics gadgets like television, cassette recorder etc.

Transformer can also be used in power stations to produce very high voltages from national grid

Types of transformers

Thereare two types of transformers, step up transformer and step down transformer

Step up transformer: they are the transformers that are used to increase the voltage supplied, for examples the ones used in power stations

Step down transformer: These are the transformers used to decrease the voltages supplied, example, the ones `used in our electronics gadgets, like computer, television, music instrument and many others.

Primary and Secondary coil of transformer.

In transformer there are primary and secondary coils. The primary and secondary coils of transformers determine whether the transformer is step up or step down transformers. The coils can also be called primary and secondary wound

The coils which are laminated, are wound one on top of the other to improve magnetic linkage. When A.C voltages are supplied to the primary coils, it produces a change in magnetic filed within it. This change in magnetic field links the secondary coils and therefore induces an E.M.f in it.

 Transformer equation

The magnitude of induced e.m.f (Vs) in secondary coil  is related to the e.m.f (Vp) applied  to the primary coil by the equation below:

Vs/vp =Ns/Np

Where Vs=e.m.f induced in secondary coils, vp= e.m.f applied to primary coils,  Ns=the numbers of turns in secondary coil and Np = the number of the turns in primary coils

Transformers that have Ns > Np, they are the step up transformers but the ones that have Np > Ns, they the step down transformers.

If we assume that , there is no magnetic flux leakage , so that all the flux produced by primary coils link with the secondary and there is no energy losses also the ideal equation of transformers is given as

\frac{{Vs}}{{Vp}} = \frac{{Ns}}{{Np}} = \frac{{Is}}{{Ip}}

Ip and Is are the current flowing in primary and secondary coils respectively   

Efficiency of transformers

The efficiency of transformer is measured by ratio of out put power to the input power.  And is given mathematically as E

Eficiency = \frac{{{{\bf{V}}_{\bf{S}}}{{\bf{I}}_{\bf{S}}}}}{{{{\bf{V}}_{\bf{P}}}{{\bf{I}}_{\bf{P}}}}} \times 100\%

Energy lose in transformers and how to reduce it

1. Edddy current loses in the core, which can be reduces by laminating the core.

2. Hysteresis loss, this is energy lost due to heating as magnetic domains in core realign. It can be reduced by using soft magnetic material for core, example silicon-iron. 

3.Flux Leakage: it is reduced by having efficient core design (soft iron core) to ensure that all the primary flux is linked with secondary.

4. Energy lost due to heating in the coils. This can be reduced by keeping their resistance low.

Question on transformers

A transformer which can produce 12V from 240r.m.s supply has efficiency of 80%. If the current in the secondary coil is 10A, calculate the current in the primary coil.

Solution,

Using    

The HTML Clipboard

\frac{{Efficiency}}{{100}} = \frac{{{V_S}{I_S}}}{{{V_S}{I_S}}}

where VS= 12V, IS =10A, Vp =220V  Efficiency = 80%,  and IP =?

\therefore \frac{{80}}{{100}} = \frac{{12 \times 10}}{{220 \times {I_P}}} = 80 \times 220 \times {I_P} = 120 \times 100

17600IP = 12000

{I_p} = \frac{{12000}}{{17600}} = 0.68A

Use of transformers

1. Transformer is used in production of our electronics, gadgets, to step down the current from the supply.

2. Transformer, is used in power generating station to step up the current

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