A segment of a circuit is shown in figure. $${v_R} = 5\,\,V,\,\,{v_C} = 4\sin 2t.$$ The voltage $${V_L}$$ is given by

A Manganin swamping resistance is connected in series with a moving coil ammeter consisting of a milli-ammeter and a suitable shunt in order to

The simplified block diagram of a $$10$$bit A/D converter of dual slope integrator type is shown in fig. The $$10$$-bit counter at the output is clocked by a $$1MHz$$ clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this A/D converter is approximately.

List $$-$$ $${\rm I}$$ represents the figures obtained on a $$CRO$$ screen when the voltage signals $$\,{V_X}\,\, = \,\,{V_{Xm}}\sin \,\,\omega t\,\,$$ and $$V_y^ \cdot \,\, = \,\,{V_{ym}}\sin \,\,\left( {\omega t + \Phi } \right)\,\,$$ are given to its $$X$$ and $$Y$$ plates respectively and $$\Phi $$ is changed. Choose the correct value of $$\Phi $$ from List $$-$$ $${\rm I}$$ to match with the corresponding figure of List $$-$$ $${\rm II}$$.