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 $$PMMC$$ voltmeter is connected across a series combination of a $$DC$$ voltage source $${V_1} = 2V$$ and $$AC$$ voltage source $${V_2}\left( t \right) = 3$$ $$sin(4t)$$ $$V.$$ The meter reads

The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-$$8$$ display. If $$P$$ and $$Q$$ are constants, and $$x(t)=P$$ $$sin(4t+30),$$ then $$y(t)$$ is equal to

A digital-to-analog converter with a full scale output voltage of $$3.5V$$ has resolution close to $$14mV.$$ It's bit size is _____.