# Auto Transformer

An auto transformer has one winding only Part of this winding being common to both primary and secondary. Primary and secondary windings are not electically isolated as in the case of a two winding transformer. Because of one winding. It uses less copper and hence is cheaper. It is used where transformation ratio differs little from unity. In Figure 1 step up and step down auto transformers are shown.

Figure 1. Auto Transformer (a) Step Up (b) Step Down

In Figure 1(a) AB is primary winding have N1 turns and BC is secondary winding having N2 turns. Neglecting losses, we can write:

V2 / V1 = I1 / I2 = K

Where current in section BC is (I2 - I1)

## Saving of Copper

Volume and hence weight of copper is proportional to the length and area of cross-section of the conductors, but length of conductor is proportional to the number of turns and cross-section of conductor depend on current. Hence weight of conductor is proportional to the product of current and number of turns.

Considering the Figure 1: Weight of copper in section AC is α (N1 - N2) I1 weight of copper in section BC is α N2 (I2 - I1). Total weight of copper in auto transformer is proportional to (N1 - N2) I1 + N2 (I1 - I1). Now consider a two winding transformer performing the same duty, weight of copper on its primary is proportional to N1I1 and weight of copper on its secondary is proportional to N2I2.

Total weight of copper is α (N1I1 + N2I2)

Thus

Dividing and multiplying by N1I1 we get:

Weight of copper of in auto transformer:

Wa = (I - K) weight of copper in 2-winding transformer, W2

Saving = W2 - Wa

= W2 - (I - K)W2

= W2 - W2 + KW2

= KW2

Saving = K (Weight of copper in 2-winding transformer. Hence saving will increase as "K" approches unity.

## Uses of Auto Transformer

1. As a booster: The voltage drop occurring in transmission lines can economically be compensated by the use of auto transformer.
2. In an induction motor starter, it is used to lower the applied voltage of motor at the starting.
3. It is used in furnaces for getting convenient supply.
4. It is used in electrical laboratories for having low voltages.
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