In a $$dc$$ motor running at $$2000$$ $$rpm,$$ the hysteresis and eddy current losses are $$500$$ $$W$$ and $$200$$ $$W$$ respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved.

A $$dc$$ series motor is rated $$230V,$$ $$1000$$ $$rpm,$$ $$80$$ $$A$$ (refer to Figure). The series field resistance is $$0.11\,\Omega ,$$ and the armature resistance is $$0.14\,\Omega .$$ If the flux at an armature current of $$20A$$ is $$0.4$$ times of that under rated condition, calculate the speed at this reduced armature current of $$20$$ $$A.$$

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.

In case of an armature controlled separately excited dc motor drive with closed loop speed control, an inner current loop is useful because it