A $$1000$$ $$V$$ $$DC$$ supply has two $$1-core$$ cables as its positive and negative leads: their insulation resistances to earth are $$4\,\,M\Omega $$ and $$6\,\,M\Omega $$, respectively, as shown in figure. A voltmeter with resistance $$50\,\,k\Omega $$ is used to measure the insulation of the cable. When connected between the positive core and earth, the voltmeter reads

The set-up in the figure is used to measure resistance $$R$$. The ammeter and voltmeter resistances are $$0.01$$$$\Omega $$ and $$2000$$$$\Omega $$, respectively. Their readings are $$2A$$ and $$180$$ $$V$$, respectively, giving a measured resistance of $$90$$ $$\Omega $$. The percentage error in the measurement is

A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The power angle is close to

A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.

The induced $$emf$$ is close to (line to line)