Shaskolskaya & Eltsin Problem 253
Physics
Problem
or connection in series E I₁ = —————— nr + R where E is the e.m.f of each cell, r is the resistance of each cell, and R is the external resistance. For connection in parallel E I₂ = —————— r/n + R obviously I₂ = I₁ if r R, i.e, if the resistance in the wire equals the internal resistance of a cell.Intuitive explanation
The key insight is understanding how internal resistance affects current delivery differently depending on how cells are connected. In series, internal resistances add up (), making the total opposition large—ideal when internal resistance is small compared to the load. In parallel, internal resistances combine as , reducing total opposition—ideal when you need to overcome a large external resistance without the penalty of many resistances in series. The condition reveals when both configurations deliver equal current, a useful design principle for battery systems.
Intuitive explanation
The key insight is understanding how internal resistance affects current delivery differently depending on how cells are connected. In series, internal resistances add up (), making the total opposition large—ideal when internal resistance is small compared to the load. In parallel, internal resistances combine as , reducing total opposition—ideal when you need to overcome a large external resistance without the penalty of many resistances in series. The condition reveals when both configurations deliver equal current, a useful design principle for battery systems.