At $$50\% $$ of full load, the armature current drawn by a $$d.c.$$ shunt motor is $$40$$ A when connected to a $$200$$ $$V$$ $$d.c.$$ mains. By decreasing the field flux, its speed is raised by $$20\% $$ this also causes a $$10\% $$ increase in load torque. Calculate the percentage change in field current. The armature resistance including the brushes is $$1$$ $$Ohm.$$ Neglect saturation and armature reaction.

The low voltage winding of a $$400/230V,$$ $$1$$-phase, $$50$$ $$Hz$$ transformer is to be connected to a $$25$$ $$Hz,$$ the supply voltage should be

A voltage $$V=400$$ sin $$314.16t$$ is applied to a $$1$$-phase transformer on no-load. If the no load current of the transformer is $$2\sin \left( {314.16t - {{85}^0}} \right),\,\,$$ then magnetization branch impedance will be approximately

A $$3$$-phase transformer bank consists of three identical $$2300/230$$ $$V,$$ $$15$$ $$kVA$$ single-phase transformers connected in delta/delta. The bank supplies a $$20$$ $$kVA,$$ unity $$p.f.$$ $$3$$-phase load. If one of the single-phase transformer develops a fault, and is removed, the load carried by each of the two transformers now operating in open delta will be __________$$kVA.$$