In a transformer each of the primary terminals becomes alternately positive and negative with respect to the other and the state is true about the secondary terminals If the transformer is to be used alone, the polarity is not important but if the transformer is to be used in parallel with another the instantaneous polarity is important because the terminals having identical instantaneous polarity have to connected together.

Refer Figs. 59 and 60. The terminals of the high voltage (h.v.) winding (i.e. H_{1} and H_{2}) and the terminals of the low voltage (l.v.) winding (i.e. X_{1} and X_{2}) are so marked that when the instantaneous voltage is directed from H_{1} and H_{2} in the high voltage winding, it is directed from X_{1} to X_{2} in the low voltage winding. In other words if the high voltage terminals H_{1} is positive with respect to H_{2} at any instant when the low voltage terminal X_{1} will be positive with respect to X_{2} at the same instant. It follows that when the terminals are arranged as in Fig. 59 the polarity is subtractive whereas the additive polarity is represented as in Fig. 60.

- One h.t. and one l.t. terminals are joined together. A voltmeter is placed between the remaining two terminals.
- A convenient moderate voltage is impressed on the h.t. winding.

If the voltage V’, is ‘greater’ that the applied voltage V, then the transformer has ‘additive’ polarity.

If V’ is less ‘less’ than V, the transformer has ‘subtractive’ polarity.

The terminals are then marked accordingly.

**Example 49. ***A load of 6 kW is supplied by an auto-transformer at 120 V and at unity power factor. If the primary voltage is 240 V, determine :*

*(i) **Transformation ratio*

*(ii) **Secondary current*

*(iii) **Primary current*

*(iv) **Number of turns across secondary if the total number of turns is 280.*

*(v) **Power transformed, and*

*(vi)**Power conducted directly from supply mains to load.*

**Solution. **Load supplied = 6 kW

**Example 51. ***A 4-kVA single-phase 50-Hz transformer has a full load efficiency of 95.5% and iron loss of 45 W. The transformer is now connected as an auto-transformer to 220 V supply. If it delivers 4 kW load at unity power factor to a 110 V circuit, calculate the efficiency of the operation and the current drawn by the high-voltage side.*

**Solution. **In Fig. 63 shows the connections for a 2-winding transformer. In Fig. 64 the same unit has been connected as an auto-transformer to a 220 V supply. Since the two-windings are connected in series, hence voltage across each is 110 V.

In both connections the iron loss would remain the same. Since the auto-transformer windings will each carry but half the current as the conventional two-winding transformer, the copper losses will be 1/4^{th} of previous value.

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