The core of two-winding transformer is subjected to a magnetic flux variation as indicated in the figure.

The induced $$emf$$ $$\left( {{e_{rs}}} \right)$$ in the secondary winding as a function of time will be of the form

Three single-phase transformers are connected to form a $$3$$-phase transformer bank. The transformers are connected in the following manner.

The transformer connection will be represented by

A single-phase $$50$$ $$kVA,$$ $$250$$ $$V/500V$$ two winding transformer has an efficiency of $$95\% $$ at full load, unity power factor. If it is reconfigured as a $$500V/750V$$ auto-transformer, its efficiency at its new rated load at unity power factor will be

Two transformers are to be operated in parallel such that they share load in proportion to their $$kVA$$ ratings. The rating of the first transformer is $$500$$ $$kVA$$ and its $$pu$$ leakage impedance is $$0.05$$ $$pu.$$ If the rating of second transformer is $$250$$ $$kVA,$$ its $$pu$$ leakage impedance is