Capacitors in Series and Parallel

A capacitor is an electronic device that acts as a store of charge. It is typically pictured as two metal plates facing each other, with a wire connected to each, as shown below.

It is connected to a source of voltage, ac or dc. If the voltage is ac then the capacitor is repeatedly charged and discharged. If the voltage is dc, then the capacitor is charged to a certain constant voltage,with the relationship between the charge stored on the capacitor and the voltage across it being governed by the relationship,, whereis the capacitance of the capacitor in question, taken to be constant for that capacitor.

Capacitors in Parallel

The capacitance of capacitors in parallel is given by

Proof: Because the capacitors are in parallel the voltage across them is the same, and the total charge on the pair is the sum of the charges, so (1).

andfor each capacitor, andfor the pair. Sub these into (1) to get

and divide byto get

Capacitors in Series

Because the capacitors are in series, charge that flows from one capacitor must flow on to the other so the charge on each capacitor is the same, and (2).

From the three equations above we getandSub these into (2) to get

then divide byto get