A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2\,\,\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {\rm I}_{NL}^2.$$ The power dissipated in the non-linear resistance is

An energy meter connected to an immersion heater (resistive) operating on an $$AC$$ $$230V,$$ $$50$$ $$Hz,$$ $$AC$$ single phase source reads $$2.3$$ units ($$kWh$$) in $$1$$ hour. The heater is removed from the supply and now connected to a $$4000$$ $$V$$ peak to peak square wave source of $$150$$ $$Hz.$$ The power in $$kW$$ dessipated by the heater will be

Two wattmeter's, which are connected to measure the total power on a three-phase system supplying a balanced load, read $$10.5$$ $$kW$$ and $$–2.5$$ $$kW$$ respectively. The total power and the power factor respectively are

A single-phase load is connected between $$R$$ and $$Y$$ terminals of a $$415$$ $$V,$$ symmetrical, $$3$$-phase, $$4$$-wire system with phase sequence $$RYB$$. A wattmeter is connected in the system as shown in figure. The power factor of the load is $$0.8 $$ lagging. The wattmeter will read