Two ac sources feed a common variable resistive load as shown in Fig. Under the maximum power transfer condition, the power absorbed by the load resistance $${R_L}$$ is

In Fig. the potential difference between points $$P$$ and $$Q$$ is

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

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