A $10$ kVA, $480/120$ V single$-$phase transformer is used as an autotransformer, connecting a $600$ V distribution line to a $480$ V load. The following data are obtained when tested as a conventional transformer, taken from the primary $(480$ V$)$ side of the transformer:

a$)$ Find the per$-$unit equivalent circuit of the transformer when connected in a conventional manner. What is the efficiency of the transformer under nominal conditions and a unitary power factor? What is the voltage regulation under these conditions?

b$)$ Draw the connections of the transformer when used as a $600/480$ V step$-$down autotransformer.

c$)$ What is the nominal value in KVAs of the transformer when used with the autotransformer connection?

d$)$ Answer the question in part a$)$ for the connection as an autotransformer.