Discussion
A 240 V/120 V, 12 kVA transformer has full load unity power factor efficiency of 96.2%. It is connected as an autotransformer to feed a load at 360 V. What would be the rating of the autotransformer at 0.85 power factor lagging?
Answer: B
When a two winding transformer is reconnected as an autotransformer, the kVA it can handle is larger than its nameplate rating, because only part of the power is transformed (the rest is conducted directly). The two windings are 240 V and 120 V, and to feed a load at 360 V they are connected in series (additive).
\[ \begin{aligned} \text{Auto kVA} \\ &= \text{kVA}_{2\text{-winding}} \times \frac{V_{high}}{V_{high} - V_{low\,side}} \\ &= 12 \times \frac{360}{360 - 240} = 12 \times 3 \\ &= 36\ \text{kVA} \end{aligned} \]
The rating in kVA does not depend on the load power factor, which only decides how many kW the 36 kVA can deliver (about 30.6 kW at 0.85), and the efficiency data is not needed. The answer is 36 kVA, option B.
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