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 sampling wattmeter (that computes power from simultaneously sampled values of voltage and current) is used to measure the average power of a load. The peak to peak voltage of the square wave is $$10V$$ and the current is triangular wave of $$5A$$ $$p$$-$$p$$ as shown in the figure. The period is $$20$$$$ms$$. The reading in $$W$$ will be

$${R_1}$$ and $${R_2}$$ are the opposite arms of $${R_3}$$ and $${R_4}$$ of a wheat stone bridge. The source voltage is applied across $${R_1}$$ and $${R_3}$$ under balanced conditions, which one of the following is true?