Capacitor problem how to find out whether a capacitor with different dielectric media is combination of parallel or series capacitors? 
Or how one can determine equipotential line in capacitors with different dielectric media? 
 A: If the two dielectrics are stacked (the electric field between the plates is normal to the interface of the two dielectrics), this is equivalent to two series connected capacitors, one for each dielectric and with the capacitance for each determined by the individual dielectric constant, dielectric thickness (which can be different for each), and the plate area (must be the same for both).  Why?  Imagine inserting two additional plates in between the two dielectrics and it should be clear.
If the two dielectrics are side by side (the electric field between the plates is parallel to the interface of the two dielectrics), this is equivalent to two parallel connected capacitors, one for each dielectric and with the capacitance for each determined by the individual dielectric constant, the dielectric thickness (must be the same for both), and only the plate area in contact with either dielectric (which can be different for each).
A: Probably you know:


*

*Parallel configuration: $C_{tot} = C_1 + C_2$.

*Serial configuration: $\frac{1}{C_{tot}} = \frac{1}{C_1} + \frac{1}{C_2}$.

*Dielectric medium: $C_j \to \epsilon_r \cdot C_j$ for $j=1,2$.


Now just replace the $C_j$'s in the first and second formula with $\epsilon_r \cdot C_j$. 
