Series grouping (n cells, each emf epsilon, internal resistance r): Total emf = nepsilon. Total internal R = nr. I = nepsilon/(R + nr). Best when R >> r (external resistance dominates). Parallel grouping (n identical cells): Total emf = epsilon. Total internal R = r/n. I = epsilon/(R + r/n). Best when R << r. Mixed grouping (m rows, n cells per row): I = mnepsilon/(nR + mr). For maximum current: nR = mr, or n/m = r/R. This gives I_max = (mn)^(1/2) * epsilon / (2*sqrt(rR)). The mixed grouping is tested when the problem specifies a fixed total number of cells.
Part of JES-03 — Current Electricity: Ohm's Law, Kirchhoff's & Circuits
Grouping of Cells
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