19. Given that $A$ is a moving point on the parabola $y^{2}=2 x$, and the fixed point $B(2,0)$, a circle $\odot C$ is constructed with $A B$ as its diameter. If the chord length of the circle $\odot C$ intercepted by the line $l$ : $x+k y-\frac{3}{2}=0$ is a constant, find this chord length and the value of the real number $k$.
19. Let the moving point $A\left(x_{0}, y_{0}\right)\left(y_{0}^{2}=2 x_{0}\right)$ on the parabola. Then the equation of the circle with diameter $A B$ is
$$
\left(x-x_{0}\right)(x-2)+\left(y-y_{0}\right) y=0 \text {. }
$$

Let the line $l$ intersect the circle at points $P_{1}\left(x_{1}, y_{1}\right)$ and $P_{2}\left(x_{2}, y_{2}\right)$,
By combining equation (1) with the line equation $x+k y-\frac{3}{2}=0$, we get
$$
4\left(1+k^{2}\right) y^{2}+4\left(k x_{0}-y_{0}-k\right) y+2 x_{0}-3=0 .
$$

Thus, $y_{1}+y_{2}=\frac{-k x_{0}+y_{0}+k}{1+k^{2}}, y_{1} y_{2}=\frac{2 x_{0}-3}{4\left(1+k^{2}\right)}$.
By $y_{0}^{2}=2 x_{0}$ and the distance formula between two points, we get
$$
\begin{array}{l}
\left|P_{1} P_{2}\right|=\sqrt{\left(1+k^{2}\right)\left(y_{1}-y_{2}\right)^{2}} \\
=\sqrt{\frac{k^{2} y_{0}^{4}-4 k y_{0}^{3}-8 k^{2} y_{0}^{2}+8 k y_{0}+16 k^{2}+12}{4\left(1+k^{2}\right)}} .
\end{array}
$$

Let $k=0$, we get $\left|P_{1} P_{2}\right|=\sqrt{3}$.
Therefore, the chord length is $\sqrt{3}$ when $k=0$.