How can we take dielectric medium kept between the capacitor plates as capacitors in series and solve for effective capacitance?

Question

My book says that the charge induced on the dielectric slab kept between the parallel plates is given $Qp=Q(1-1/K)$ where $K$ is the dielectric constant and $Q$ is the charge on the capacitor.

I have seen that in some books equivalent capacitance of capacitors with dielectric in the middle partially filled is found by taking 2 capacitors in series combination. But I thought that to take 2 capacitors in series, they must have same magnitude of charges. But it doesn't seem like the dielectric surface has the same charge as that of the capacitors.

Am I wrong or is the condition for series not quite straightforward as I assumed?

Answer 1

Imagine a capacitor with parallel plates, if you put a very thin conducting plate somewhere in between , it does not change the C, and you can consider it as two capacitors in a row. Now insert the dielectricum in one of them.