The capacitance of a parallel plate capacitor without any medium between its plates is given by [latex]C_{0}=\frac{\varepsilon _{0}A}{d}[/latex]

When a dielectric completely fills the space between the plates of the capacitor, the capacitance increases K times, where K is the dielectric constant (relative permitivity) of the dielectric.

[latex]C_{m}=\frac{K\varepsilon _{0}A}{d}[/latex]

If a dielectric slab of thickness t (<d) is introduced between the plates, the capacitance becomes [latex]C=\frac{\varepsilon _{0}A}{d-t\left ( 1-\frac{1}{K} \right )}[/latex]

OR

[latex]C=\frac{\varepsilon _{0}A}{d\left \{ \frac{t}{d}\left ( 1-\frac{1}{K} \right ) \right \}}[/latex]

OR

[latex]C=\frac{C_{0}}{\frac{t}{d}\left ( 1-\frac{1}{K} \right )}[/latex]

In each case the capacitance increases with the introduction of a dielectric in between the plates

http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter27/chapter27.html

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