Two parallel plate capacitors X and Y are connected in series to a $6\text{ V}$ battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant $4$. (a) Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is $4\text{ }\mu\text{F}$. (b) Calculate the potential difference across the plates of X and Y.