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 DC ammeter has a resistance of $$0.1$$$$\Omega $$ and its current range is $$0$$ – $$100A.$$ If the range is to be extended to $$0$$ –$$500A,$$ the meter requires the following shunt resistance

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

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