A diode whose terminal characteristics are related as $${i_D} = {{\rm I}_S}\,{e^{{V \over {{V_T}}}}},\,$$ where $${{\rm I}_S}$$ is the reverse saturation current and $${V_T}$$ is thermal voltage ($$25$$ $$mV$$) is biased at $${i_D} = 2\,mA.$$ Its dynamic resistance is _______.

In the single phase diode bridge rectifier shown in the figure, the load resistor is $$R = 50\,\Omega .$$ The source voltage is $$V=200$$ $$sin$$ $$\omega t,$$ where $$\omega = 2\pi \, \times \,50\,rad/sec.$$ The power dissipated in the load resistor $$R$$ is

Figure shows as electronic voltage regulator the zener diode may be assumed to require a minimum current of $$25$$ $$mA$$ for satisfactory operations. The value of $$R$$ required for satisfactory voltage regulation of the circuit is