COMBINATIONS OF CAPACITORS
When a capacitor charges up, work must be done by an external force (for example
a battery). This increases the potential energy stored by the capacitor. The potential
energy stored is given by the formula
Capacitors are often arranged in combination in electric circuits. Let’s review two
types of arrangements: the parallel combination and the series combination.
A collection of capacitors are said to be in parallel if they all share the same
potential difference. The following diagram shows two capacitors wired in
parallel.
The top plates are connected by a wire and form a single equipotential; the same is
true for the bottom plates. Therefore, the potential difference across one capacitor
is the same as the potential difference across the other capacitor.
If we want to find the capacitance of a single capacitor that would perform the
same function as this combination, and if the capacitances are C 1 and C 2 , then the
charge on the first capacitor is Q 1 = C 1 ∆V and the charge on the second capacitor
is Q 2 = C 2 ∆V. The total charge on the combination is Q 1 + Q 2 , so the equivalent
capacitance, CP, must be