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 ______.

Assuming the diodes to be ideal in the figure, for the output to be clipped, the input voltage $${V_i}$$ must be outside the range

The transistor in the given circuit should always be in active region. Take $${V_{CE\left( {sat} \right)}} = 0.2\,\,V,\,\,\,{V_{BE}} = 0.7\,\,V.\,\,\,$$ The maximum value of $${R_C}$$ in $$\Omega $$ which can be used, is __________.

An oscillator circuit using ideal op-amp and diodes is shown in the figure.

The duration for $$+ve$$ part of the cycle $$\Delta {t_1}$$ and for $$-ve$$ part is $$\Delta {t_2}.$$ The value of $$e$$ $${{\Delta {t_2} - \Delta {t_1}} \over {RC}}$$ will be _______.