Two conducting parallel plates have area A, are separated by distance d, and are filled with a dielectric material of constant K1. The capacitance of this system is C. A student plans to replace the dielectric K1 with a second dielectric, K2, where K2=2K1. However, the student only has half the volume of dielectric material to fully replace K1. So the student fills half the gap with K1 and half with K2. Both K1 and K2 have a cross sectional area of A, but a thickness of d/2, as shown in the diagram above.
In terms of C, what is the new capacitance of this modified system?