An ideal transformer has a linear $$B-H$$ characteristic with a finite slope and a turns ratio of $$1:1.$$ The primary of the transformer is energized with an ideal current source, producing the signal i as shown in figure. Sketch the shape (neglecting the scale factor) of the following signals, labeling the time axis clearly

$$(a)$$ $$\,\,\,\,\,$$ the core flux $${\phi _{oc}}$$ with the secondary of the transformer open
$$(b)$$ $$\,\,\,\,\,$$ the open-circuited secondary terminal voltage $${V_2}\left( t \right).$$
$$(c)$$ $$\,\,\,\,\,$$ the short-circuited secondary current $${i_2}\left( t \right)$$
$$(d)$$ $$\,\,\,\,\,$$ the core flux $${\phi _{sc}},$$ with the secondary of the transformer short-circuited.

Two single phase transformers $$A$$ and $$B$$ have the following parameters.
Transformer $$A$$: $$400V/200V,$$ $$10$$ $$kVA,$$ percentage resistance and percentage reactance are $$3\% $$ and $$4\% $$ respectively.
Transformer B: $$5$$ $$kVA,$$ $$400V/200V,$$ percentage resistance and percentage reactance are $$4\% $$ and $$3\% $$ respectively.
These two transformers are connected in parallel and they share a common load of $$12$$ $$kW$$ at a power factor of $$0.8$$ lag. Determine the active and reactive power delivered by transformer $$A.$$

In a $$50$$ $$KVA,$$ $$11$$ $$KV/400$$ $$V$$ transformers, the iron and copper losses are $$500$$ $$W$$ and $$600$$ $$W$$ respectively under rated conditions. Calculate the efficiency on unity power factor at full load. Find the load for maximum efficiency and the iron and copper losses corresponding to this load.