Consider a circuit consisting of a capacitor \( (20 \, \mu \text{F}) \), 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 \( \alpha \times 10^{-3} \, \text{s} \). The value of \( \alpha \) is ______.
