Generally we have seen in basic model of transformer there are two windings. One is primary winding and one is secondary winding. But there is another type of transformer which has only one winding. This single winding serves the purpose of both primary and secondary winding. The transformer which uses such single winding is referred to as auto transformer.
Now one question may arise in your mind – how does autotransformer work with one single winding instead of two separate windings ?
We know that in two winding transformer there is no direct connection between the primary and secondary. They are interlinked by common magnetic path. Here in autotransformer the single winding is connected both electrically and magnetically. One winding which serves purpose of both primary and secondary is divided into two parts – common winding part and series winding part.
Say N1 is the total number of turns of autotransformer winding AB. Let's voltage V1 is applied in between terminal A & B as shown. Similarly N2 be the number of turns in secondary winding and let it be tapped at C. Now if we measure voltage between B & C we will get secondary voltage V2. As the primary voltage applied across the terminal AB which has total number of turns N1, voltage per turn of the winding will be V1/N1. As we tap secondary terminal from point C the voltage appeared across B & C is nothing but N2V1/N1. As BC portion of the winding is considered as secondary, it can easily be understood that value of constant k is nothing but turns ratio or the voltage ratio of that Auto Transformer.
Autotransformer is constructionally more or less similar to potential divider. Autotransformer works in different ways. Autotransformer can set up a voltage whereas potential divider can do so. In potential divider the output current is always is always reduced but in step down autotransformer as output voltage is reduced output current is proportionally increased .In potential divider the power is transferred to the load by conduction whereas in autotransformer power is transformed to the load partly by conduction and partly by induction. In potential divider total power is transferred via conduction contributing huge I2R losses but in autotransformer I2R losses are much less because the power is transformed not entirely by conduction rather partly by conduction. In ideal autotransformer as there is no loss we can say V1 × I1 = V2 × I2. So V2/V1 = I1/I2 = K, the transformation ratio of a conventional transformer.