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 $\_\_\_\_$。