You have two identical capacitors and an external potential source.
a. Compare the total energy stored in capacitor when they are connected to the applied potential in series and in parallel.
b. Compare the maximum amount of charge stored in each case.
c. Energy storage in a capacitor can be limited by the maximum electric field between the plates. What is the ratio of the electric field for the series for parallel combinations?

Explanation

Let the applied voltage be `V`. Let each capacitor have capacitance `C`.
`U=1/(2)CV^(2)`
for a single capacitor with voltage `V`.
a. Series: Voltage across each capacitor is `V/2`. The total energy stored is
`U_(s) = 2((1)/(2)C[V//2]^(2)) = (1)/(4)Cv^(2)`
Parallel: Voltage acroos each capacitor is `V`. The energy stored is
`U_(p) = 2((1)/(2)CV^(2))= CV^(2)` or `U_(P) = 4U_(s)`
b. `Q = CV` for a single capacitor with voltage `V`.
`Q_(s) = 2(C[V//2]) = CV`
`Q_(p) = 2(CV) = 2CV` c. `E = V//d` for a capacitor with voltage `V`.
`E_(s) = V//2d, E_(p) = V//d, E_(p) = 2E_(s)`