Capacitors in Parallel

Capacitors are said to be connected in PARALLEL when all of their first plates are joined together to one single common terminal A (connected onward to the applied source), and all of their second plates are joined together to a second common terminal B (typically earthed). Every capacitor in such a bank therefore experiences the SAME potential difference V across it -- but, unlike the series case, there is no requirement at all that they carry the same charge; each is free to hold whatever charge its own individual capacitance dictates at that shared voltage.

If a total charge Q is supplied at terminal A, it distributes itself among the parallel capacitors in direct proportion to each one's own capacitance: $Q=Q_1+Q_2+Q_3=C_1V+C_2V+C_3V$ (using $Q_i=C_iV$ for each, since all share the same V). Defining the equivalent parallel capacitance as $C_P=Q/V$ and substituting gives $C_PV=C_1V+C_2V+C_3V$; the common factor V cancels from every term, leaving simply $C_P=C_1+C_2+C_3$ for three capacitors in parallel -- generalising directly to $C_P=C_1+C_2+\cdots+C_n$ for $n$ capacitors in parallel: the equivalent parallel capacitance is nothing more than the plain SUM of the individual capacitances. Unlike the series case, adding another capacitor to a parallel bank can only ever GROW the overall equivalent capacitance, making $C_P$ always LARGER than even the single largest capacitance already present in the group. If all $n$ capacitors happen to be identical, each of value $C$, this simplifies to $C_{eq}=nC$. …