Electromechanical Devices

TransformersLecture 5

Transformers

A transformer is a device which uses the phenomenon of mutual induction to change the values of alternating voltages and currents.

One of the main advantages of a.c. transmission and distribution is the ease with which an alternating voltage can be increased or decreased by transformers.

Losses in transformers are generally low and thus efficiency is high. Being static they have a long life and are very stable.

Transformers range in size from the miniature units used in electronic applications to the large power transformers used in power stations. The principle of operation is the same for each.

A transformer is represented in Figure (a) as consisting of two electrical circuits linked by a common ferromagnetic core. One coil is termed the primary winding which is connected to the supply of electricity, and the other the secondary winding, which may be connected to a load.

A circuit diagram symbol for a transformer is shown in Figure (b).

Transformer principle of operation

When the secondary is an open-circuit and an alternating voltage V1 is applied to the primary winding, a small current—called the no-load current I0 —flows, which sets up a magnetic flux in the core. This alternating flux links with both primary and secondary coils and induces in them e.m.f.’s of E1 and E2 respectively by mutual induction. The induced e.m.f. E in a coil of N turns is given by

volts

where d/dt is the rate of change of flux. In an ideal transformer, the rate of change of flux is the same for both primary and secondary and thus E1/N1 = E2/N2, i.e. the induced e.m.f. per turn is constant.

Assuming no losses, E1 =V1 and E2 =V2

Hence

(1)

Transformer principle of operation

V1/V2 is called the voltage ratio N1/N2 is called the turns ratio, or the ‘transformation ratio’ of the transformer. If N2 is less than N1 then V2 is less than V1 and the device is termed a step-down transformer. If N2 is greater than N1 then V2 is greater than V1 and the device is termed a step-up transformer.

Transformer principle of operation

When a load is connected across the secondary winding, a current I2 flows. In an ideal transformer losses are neglected and a transformer is considered to be 100% efficientHence input power = output power, or V1 I1 = V2 I2i.e., in an ideal transformer, the primary and secondary volt-amperes are equal.Therefore, (2)From equations (1) and (2)

Transformer principle of operation

The rating of a transformer is stated in terms of the volt-amperes that it can transform without overheating.Therefore, the transformer rating is either V1 I1 or V2 I2

Example 5.1

A transformer has 500 primary turns and 3000 secondary turns. If the primary voltage is 240 V, determine the secondary voltage, assuming an ideal transformer.

Solution

For an ideal transformer, voltage ratio = turns ratio

Or

Example 5.2

An ideal transformer with a turns ratio of 2:7 is fed from a 240 V supply. Determine its output voltage.

Solution

A turns ratio of 2:7 means that the transformer has 2 turns on the primary for every 7 turns on the secondary (i.e. a step-up transformer).

Thus

For an ideal transformer,

or

Example 5.3

An ideal transformer has a turns ratio of 8:1 and is supplied at 240 V when the primary current is 3 A. Calculate the secondary voltage and current

Solution

A turns ratio of 8:1 means , i.e. a step-down transformer

or

For an ideal transformer, voltage ratio = turns ratio

Example 5.4

An ideal transformer, connected to a 240 V mains, supplies a 12 V, 150 W lamp. Calculate the transformer turns ratio and the current taken from the supply.

Solution

V1 = 240 V, V2 = 12 V,

Turns ratio

Therefore

Hence current taken from the supply,

Example 5.5

A 5 kVA single-phase transformer has a turns ratio of 10:1 and is fed from a 2.5 kV supply. Neglecting losses, determine (a) the full-load secondary current, (b) the minimum load resistance which can be connected across the

secondary winding to give full load kVA, (c) the primary current at full load kVA.

Solution

(a) and V1 = 2.5 kV = 2500 V

Since ,

secondary voltage

The transformer rating in volt-amperes = V2 I2 (at full load),

i.e.,

Hence full load secondary current

Example 5.5

(b) Minimum value of load resistance,

(c) ,

Therefore