Two identical capacitors are connected in series across a battery. How does the energy stored in this combination compare to the energy stored in a single capacitor connected across the same battery?

Core Concept

For capacitors in series, the equivalent capacitance is Cₑq = C/2 (for two identical capacitors). The energy stored in a capacitor is U = ½CV². For a single capacitor, Uₛingle = ½CV². For the series combination, Uₛeries = ½(C/2)V² = ¼CV². Therefore, the series combination stores half the energy of a single capacitor when connected to the same battery.