The sinusoidal ac source in the figure has an rms value of $${{20} \over {\sqrt 2 }}\,V.$$ Considering all possible values of $${R_L},\,\,$$ the minimum value of $${R_s}$$ in $$\Omega $$ to avoid burnout of the Zener diode is ______.

The figure shows the circuit of a rectifier fed from a 230 V (rms), 50Hz sinusoidal voltage source. If we want to replace the current source with a resistor so that the rms value of the current supplied by the voltage source remains unchanged, the value of the resistance (in ohms) is __________ (Assume diodes to be ideal)

The $$i$$-v characteristics of the diode in the circuit given below are $$$i = \left\{ {\matrix{ {{{v - 0.7} \over {500}}A,} & {v \ge 0.7\,V} \cr {0A,} & {v < 0.7\,V} \cr } } \right.$$$

The current in the circuit is

Assuming that the diodes an ideal in the given circuit, the voltage $${V_0}$$ is