# Electrotechnology

Lab Report

Aim:

To investigate and analyse single-phase transformers in a circuit

Objectives:

To determine the approximate equivalent circuit of a single-phase transformer so the transformer can be modelled, predicted and analysed.

Equipment:

TecQuipment electrical machines teaching unit NE8010 or NE8013 B-phase transformer (EMTU-TT01)

One Hameg HM-8115-2 Power meter

Wires

Introduction and theory of Transformers:

Transformers are simple, energy transfer devices that are widely used for power transmission. Depending on how well they are made and designed, they can be nearly 100% efficient.

The most basic of single-phase transformers has two coils or windings on it, one called the primary winding and one called the secondary winding, both of which are made out of conductive material. These windings are attached to the limbs of the transformer core as shown in the pic of an ideal transformer. The core itself is made out of magnetic material.

Pic of ideal transformer

The two windings have no conductive connection between them and are kept separate, usually by the length of the yoke and also by insulation around the conductive material. In other words they are not linked electrically but they are linked magnetically. On the input side of the transformer (primary winding) a varying electrical current is applied. This varying current produces magnetic flux that flows around the core. This varying magnetic flux causes the secondary winding to induce an electromotive force (EMF) and this will cause a current to flow from the secondary winding. This is called mutual inductance, when the change in current in one winding results in an induction of voltage in the other winding. The varying electrical current is most commonly alternating current but pulsed continuous current can be used as well to make the transformer work.

According to the laws of conservation of energy, the energy input equals energy output. For ideal transformers we assume their efficiency is 100%, and as most well designed transformers are highly efficient (95-99.5%) we can model them as an ideal transformer.

One use of transformers is to step up and step down voltages. This is when the electrical energy on the primary winding has to be stepped up or stepped down to a different voltage level on the secondary winding. The ratio of the number of turns on the winding on the primary and secondary side determines the voltage output on the secondary winding. From Faraday's law of electromagnetic induction we know:

V1 = N1 dÖ/dt and

V2 = N2 dÖ/dt

Where V1 and V2 are the primary and secondary voltages respectively, N1 and N2 are the number of turns on the primary and number of turns on the secondary windings respectively and dÖ/dt is the rate of change of flux.

By equating the two we get:

V1/V2 = N1/N2

This tells us the winding with the greatest number of turns has the higher voltage and vice versa, i.e. voltage is proportional to the number of turns. As there are a greater number of turns, there is higher magnetic flux and this accounts for the greater voltage, the opposite is also true, the winding with the least number of turns has lower magnetic flux and the smaller voltage.

Also due to the law of conservation of energy and the fact that an ideal transformer is 100% efficient:

P1 = P2 But P = IV

I1V1 = I2V2

V1/V2 = I2/I1

Therefore:

N1/N2 = I2/I1

This tells us that the winding with the greatest number of turns has the lower current and vice versa, i.e. there is an inverse relationship between current in a winding and number of turns in a winding.

There is another equation that links number of turns, core area, magnetic flux and voltage, assuming the transformer is ideal:

E = 4.44 B N A f

Where E is the sinusoidal root mean squared (RMS) voltage, B is magnetic flux, N is number of turns, A is cross-sectional area of the core and f is frequency. This is...

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