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 $$-$$ $${\rm II}$$.

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.

An ac voltmeter uses the circuit shown below, where the $$PMMC$$ meter has an internal resistance of $$100$$$$\Omega $$ and requires a dc current of $$1$$ $$mA$$ for full scale deflection. Assuming the diodes to be ideal, the value of $${R_s}$$ to obtain full scale deflection with $$100$$ $$V$$ (ac rms) applied to the input terminal would be

The inductance of a certain moving-iron ammeter is expressed as $$L = 10 + 3\theta - {{{\theta ^2}} \over 4}\mu H,\,\,$$ where $$\,\,\theta \,\,\,$$ is the deflection in radians from the zero position. The control spring torque in $$\,\,25\,\, \times \,\,{10^{ - 6}}\,\,\,$$ Nm/radian. The deflection of the pointer in radian when the meter carries a current of $$5A,$$ is