Consider a parallel plate capacitor formed by two plates of length $L$ and width $d$, separated by a distance $e$. There is a vacuum in between the plates. Let's note the capacitance of this arrangement $C_0$.
I insert a conducting plate of length $l=L/2$, with $D$, and thickness $e' <<e$. The position of the plate is measured by its $(x,y)$ coordinates, as shown below:
Of course if $x<0$, the conductor is not inserted at all so the capacitance remains unchanged, $C_0$.
Consider the case where the conductor is inserted partially, i.e $0<x<l$.
According to my notes, in this case the apparatus is equivalent to the arrangement of capacitors below:
I do not understand why this configuration is equivalent to the arrangement of capacitors given above.
I guess $C_1$ is the capacitor formed by the top plate and the conductor, $C_2$ the capacitor formed by the bottom plate and the conductor, and $C_3$ the capacitor formed by the conductor itself. However this leaves me confused as the capacitance for the conductor should then be
Finally, if we now consider the case where the conductor is fully inserted, i.e $l<x<L$, then apparently the capacitor arrangement changes completely and we now actually have four capacitors (2 in series, which are parallel with the other two). I don't understand why.