How do the resistance and the capacitance of the cell membrane change?

As the resistance of the cell membrane increases, its capacitance decreases.

Explanation:

As we know the plasma membrane or cell membrane has a lipid bilayer structure and many types of molecules are embedded in this structure. Due to the presence of lipids, the plasma membrane possess a high electrical resistivity that means it is less permeable to some ions. That's why some molecules need active transport mechanism to cross the membrane.

As the bilayer of the cell membrane is very thin, the accumulation of the charges on the one side of membrane imposes electrical forces to the ions present on other side of the membrane. Due to this force the Capacitance property in the membrane arises.