A Single-Phase $15-\mathrm{kVA}, 2400 / 240$ -Volt $60-\mathrm{Hz}$ Two-Winding Distribution Transformer Is Connected as an Autotransformer to Step

A single-phase $15-\mathrm{kVA}, 2400 / 240$ -volt, $60-\mathrm{Hz}$ two-winding distribution transformer is connected as an autotransformer to step up the voltage from 2400 to 2640 volts. (a) Draw a schematic diagram of this arrangement, showing all voltages and currents when delivering full load at rated voltage. (b) Find the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of this kVA rating is transformed by magnetic induction? (c) The following data are obtained from tests carried out on the transformer when it is connected as a two-winding transformer:
Open-circuit test with the low-voltage terminals excited:
Applied voltage $=240 \mathrm{~V}$ , Input current $=0.68 \mathrm{~A}$ , Input power $=105 \mathrm{~W}$ .
Short-circuit test with the high-voltage terminals excited:
Applied voltage $=120 \mathrm{~V}$ , Input current $=6.25 \mathrm{~A}$ , Input power $=330 \mathrm{~W}$ .
Based on the data, compute the efficiency of the autotransformer corresponding to full load, rated voltage, and 0.8 power factor lagging. Comment on why the efficiency is higher as an autotransformer than as a two-winding transformer.