# Suppose that three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

Apr 24, 2018

More in parallel: see below.

#### Explanation:

Parallel

Combined capacitance:

${C}_{T} = 3 C$

Stored energy:

${U}_{p a r a l l \setminus e l} = \frac{1}{2} {C}_{T} {V}_{o}^{2} = \frac{3}{2} C {V}_{o}^{2}$

Series

Combined capacitance:

$\frac{1}{C} _ T = \frac{3}{C} \implies {C}_{T} = \frac{C}{3}$

Stored energy:

${U}_{s e r i e s} = \frac{1}{2} {C}_{T} {V}_{o}^{2} = \frac{1}{6} C {V}_{o}^{2}$

$\implies {U}_{p a r a l l \setminus e l} / {U}_{s e r i e s} = \frac{\frac{3}{2} C {V}_{o}^{2}}{\frac{1}{6} C {V}_{o}^{2}} = 9$