This demonstration, again, can be used as an interactive homework problem. A partially-filled capacitor can be viewed as a pair of capacitors, one filled and the other unfilled. (Note that this is only true for geometries where the dielectric interface is approximately on an equipotential surface, as nothing then changes when the extra pair of metal plates is inserted. This same technique could be used on a partially-filled cylindrical or spherical capacitor, for example, provided the dielectric surface was cylindrical or spherical, respectively.) Use the formula for the capacitance in terms of the area of the plates, distance between the plates, and the dielectric constant to write down the capacitance of the "filled" and "empty" capacitors. Notice that the distance between the plates of each capacitor depends on the percentage k of the dielectric material, as shown in the demonstration. Then, use the formula for the equivalent capacitance of the two capacitors connected in series to derive the result in the "Details" section of the demonstration. The values of A and d is fixed and given in the "Details" section of the demonstration. You can select a value of k and a dielectric material (you will have to look up the value of the dielectric constant), and calculate the capacitance of the partially filled capacitor. Again, confirm that your result agrees with the demonstration.