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 givesThese follow from $Q_i=C_i{V}_i$, together with the connection constraints.^[ref] With $N_s$ identical units in each series string and $N_p$ such strings in parallel, $C_{\mathrm{bank}}=N_{p}C/N_s$. At terminal difference $V$, the ideal stored capacitor energy is $E=C_{\mathrm{bank}}{V}^2/2$.

For example, four $100\mu \mathrm{F}$ units arranged as two series pairs in parallel give $100\mu \mathrm{F}$ 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 $C{V}_0^2/2$, but final energy in the two capacitors is $C{V}_0^2/4$. 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.