In a single phase $$3$$ winding transformer the turns ratio for primary: secondary: tertiary windings is $$20:4:1.$$ With the lagging currents of $$50A$$ at a power factor of $$0.6$$ in the tertiary winding find the primary current and power factor.

A single phase $$6300$$ $$kVA,$$ $$50$$ $$Hz,$$ $$3300V/400V$$ distribution transformer is connected between two $$50$$ $$Hz$$ supply systems, $$A$$ and $$B$$ as shown in Fig. The transformer has $$12$$ and $$99$$ turns in the low and high voltage windings respectively. The magnetizing reactance of the transformer referred to the high voltage side is $$500\Omega .$$ The leakage reactance of the high and low voltage windings are $$1.0\Omega $$ and $$0.012\Omega $$ respectively. Neglect the winding resistance and core losses of the transformer. The Thevenin voltage of system $$A$$ is $$3300V$$ while that of system $$B$$ is $$400V.$$ the short circuit reactance of systems $$A$$ and $$B$$ are $$0.5\Omega $$ and $$0.010\Omega $$ respectively. If no power is transferred between $$A$$ and $$B,$$ so that the two system voltages are in phase, find the magnetizing ampere turns of the transformer.

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 $$A.$$