Connecting current sources in series and in parallel
The EMF of one galvanic cell is small (about 1–2 V), so cells are joined into batteries. Kirchhoff’s 1st rule: the algebraic sum of currents into and out of a node is zero (conservation of charge): ΣI = 0. 2nd rule: around a closed loop the algebraic sum of the voltage drops (IR) equals the algebraic sum of the EMFs: ΣIR = Σℰ. When n identical cells (ℰ, r) are joined in series, the battery has EMF nℰ and internal resistance nr, and I = nℰ/(R + nr); if R ≫ nr then I ≈ nℰ/R, n times the current of one cell – useful with a large external resistance. When they are joined in parallel (like terminals together) the EMF is ℰ, the internal resistance r/n and I = ℰ/(R + r/n); if R ≪ r the current is about n times that of one cell – useful with a small external resistance. If two sources are connected against each other by like terminals (ℰ₂ > ℰ₁), I = (ℰ₂ – ℰ₁)/(r₁ + r₂).
Only by calculation: tabulate the EMF and internal resistance of 3 identical cells in series and in parallel; by calculation decide which arrangement gives more current for R = 0.1 Ω and R = 30 Ω. Never short-circuit batteries or accumulators.