Part of JES-03 — Current Electricity: Ohm's Law, Kirchhoff's & Circuits

Grouping of Cells

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Series grouping (n cells, each emf epsilon, internal resistance r): Total emf = nepsilon. Total internal R = nr. I = nepsilonR+nr\frac{epsilon}{R + nr}. Best when R >> r (external resistance dominates). Parallel grouping (n identical cells): Total emf = epsilon. Total internal R = rn\frac{r}{n}. I = epsilonR+r/n\frac{epsilon}{R + r/n}. Best when R << r. Mixed grouping (m rows, n cells per row): I = mn*epsilonnR+mr\frac{epsilon}{nR + mr}. For maximum current: nR = mr, or n/m = rR\frac{r}{R}. This gives ImaxI_{max} = (mn)^12\frac{1}{2} * epsilon / (2sqrt(rR)). The mixed grouping is tested when the problem specifies a fixed total number of cells.

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