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

It is desired to measure parameters of $$230$$ $$V/115$$ $$V,$$ $$2$$ $$kVA$$, single-phase transformers. The following watt-meters are available in a laboratory:
$${W_1}:250\,\,V,\,\,\,10\,\,A,\,\,\,\,\,\,$$ Low Power Factor
$${W_2}:250\,\,V,\,\,\,5\,\,A,\,\,\,\,\,\,$$ Low Power Factor
$${W_3}:150\,\,V,\,\,\,10\,\,A,\,\,\,\,\,\,$$ High Power Factor
$${W_4}:150\,\,V,\,\,\,5\,\,A,\,\,\,\,\,\,$$ High Power Factor

The watt-meters used in open circuit test and short circuit test of the transformer will respectively be

A $$240V$$ $$dc$$ shunt motor draws $$15A$$ while supplying the rated load at a speed of $$80$$ $$rad/s$$. The armature resistance is $$0.5$$ $$ohm$$ and the field winding resistance is $$80$$ $$ohm.$$

The external resistance to be added in the armature circuit to limit the armature current to $$125\% $$ of its rated value is