Consider a circuit consisting of a capacitor $(20 \mu \mathrm{~F})$, resistor $(100 \Omega)$ and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is $10 \Omega$. The time constant of the circuit is $\alpha \times 10^{-3} \mathrm{~s}$. The value of $\alpha$ is $\_\_\_\_$

If X and Y are the inputs, the given circuit works as _________.

For the given circuit (shown in part (A)) the time dependent input voltage $v_{in}(t)$ and corresponding output $v_{o}(t)$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.

Two p-n junction diodes $D_1$ and $D_2$ are connected as shown in figure. $A$ and $B$ are input signals and $C$ is the output. The given circuit will function as a ________.