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 _______.

The forward resistance of the diode shown in figure is $$5\Omega $$ and the remaining parameters are same as those of ideal diode. The $$DC$$ component of the source current is

The cut in voltage of both Zener diode $${D_z}$$ and diode $$D$$ shown in Figure is $$0.7$$ $$V,$$ while break down voltage of the zener is $$3.3$$ $$V$$ and reverse breakdown voltage of $$D$$ is $$50$$ $$V.$$ the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage ($${V_0}$$) are

The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is