A current of $$ - 8 + 6\sqrt 2 \left( {\sin \,\omega t + {{30}^0}} \right)\,\,A$$ is passed though three meters. They are a center zero $$PMMC$$ meter, true $$r.m.s$$ meter and moving $${\rm I}$$ron instrument. The respective reading (in $$A$$) will be

The time/div and voltage/div axes of an oscilloscope have been erased. A student connects a 1kHz, 5V p-p square wave calibration pulse to channel-1 of the scope and observes the screen to be as shown in the upper trace of the fig. An unknown signal is connected to channel -2 (lower trace ) of the scope. If the time/div and V/div on both channels are the same, the amplitude (p-p) and period of the unknown signal are respectively.

A $$200/1$$ current transformer $$(CT)$$ is wound with $$200$$ turns on the secondary on a toroidal core. When it carries a current of $$160$$ $$A$$ on the primary, the ratio and phase errors of the $$CT$$ are found to be $$-$$ $$50$$% and $$30$$ minutes respectively. If the number of secondary turns is reduced by $$1$$ the new ratio error (%) and phase error (min) will be respectively.

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