Series & Parallel Capacitors

Series Capacitors

When the capacitors are connected in series, the total capacitance is less than the smallest capacitance value.

Both capacitors store the same amount of charge. The voltage across each one depends on its capacitance value (U = Q/C). By Kirchoff's voltage law, the sum of the capacitor voltages equals the source voltage (U_s = U₁ + U₂). Since U = Q/C and Q = Q_T = Q₁ = Q₂ the relationship for two capacitors in series is derived. It can be extended to any number of capacitors in series as shown in the diagram. 

Parallel Capacitors

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances. When the switch is closed, part of the total charge is stored by C₁ and part is stored by C₂. The portion of the total charge that is stored by each capacitor depends on its capacitance value (Q = CU). Since the voltage across both capacitors is the same, the larger capacitor stores more charge. The charges stored by both capacitors equals the total charge that was delivered from the source (Q_T = Q₁ + Q₂). Because all the voltages are the same, the C_T is the sum of both capacitances.