An ideal capacitor is charged to a voltage $${V_0}$$ and connected at $$t=0$$ across an ideal inductor $$L.$$ (The circuit now consists of a capacitor and inductor alone). If we let $${\omega _0} = 1/\sqrt {LC} ,$$ the voltage across the capacitor at time $$t>0$$ is given by

A variable $$'w'$$ is related to three other variables $$x, y, z$$ as $$w=xy/z.$$ The variables are measured with meters of accuracy$$ \pm $$ $$0.5$$% reading, $$ \pm 1\% $$ of full scale value and $$ \pm 1.5\% $$ reading the actual readings of the three meters are $$80,20$$ and $$50$$ with $$100$$ being the full scale value for all three. The maximum uncertainty in the measurement of $$'w'$$ will be

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.