= Capacitor bank
A capacitor bank is a connected collection of <capacitors> designed to supply a required equivalent <capacitance>, stored <electrostatic energy> or electrical response. Its behavior depends on the connections, not just the number of components. Parallel branches share a terminal <electric potential difference>; a simple series string carries the same magnitude of separated <electric charge> on each initially neutral intermediate node.
For linear ideal <capacitors>, adding charge in parallel and potential differences in series gives
$$
C_{\parallel}=\sum_iC_i,\qquad
\frac1{C_{\rm series}}=\sum_i\frac1{C_i}.
$$
These follow from $Q_i=C_iV_i$, together with the connection constraints.<University Physics Volume 2 by Samuel J. Ling and others>[Section 8.2, series and parallel combinations]{ref} With $N_s$ identical units in each series string and $N_p$ such strings in parallel, $C_{\rm bank}=N_pC/N_s$. At terminal difference $V$, the ideal stored <capacitor energy> is $E=C_{\rm bank}V^2/2$.
For example, four $100\,\mathrm{\mu F}$ units arranged as two series pairs in parallel give $100\,\mathrm{\mu F}$ overall. At $500\,\mathrm V$, equal sharing would place $250\,\mathrm V$ across each unit and store $12.5\,\mathrm J$ altogether. Capacitance and voltage sharing are separate design questions: unequal <capacitances>, initial charges and leakage can prevent equal sharing. A component's stated rating is not by itself evidence that a series string divides the applied difference equally.
A charge-sharing experiment illustrates why connecting charged components is a transient process. Connect one ideal <capacitor> $C$ initially at $V_0$ to an identical uncharged one through a <resistor>. Charge conservation gives final common difference $V_0/2$. Initial energy is $CV_0^2/2$, but final energy in the two <capacitors> is $CV_0^2/4$. The remaining energy is dissipated during current flow in this model; summing the final <capacitances> does not explain away the transient loss.
For a pulsed load, a bank's terminal response additionally depends on connection <inductance> and resistance. The ideal <capacitance> specifies charge storage, while those other properties help determine how quickly stored energy can be delivered. Comparing current and terminal <electric potential difference> during discharge tests that distinction.
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