Series and Parallel Circuits

Objective: Calculate branch voltage, current splitting, and equivalent resistance.

Parallel components connect across the same two nodes, so each branch has the same potential difference in the ideal circuit model. Total current entering a junction equals the sum of branch currents leaving it. For two resistors, 1/R_eq = 1/R₁ + 1/R₂. A 6 Ω and 3 Ω pair across 12 V carries 2 A and 4 A in its branches, for 6 A total and 2 Ω equivalent resistance. Adding a conducting parallel path lowers equivalent resistance when the source voltage stays fixed, increasing total source current. An open branch does not necessarily stop current in other branches. Real source and wire limits may affect voltages and currents.

Objective: Apply series and parallel circuits to calculations, evidence, and specified situations.

Ideal series components share one current path, so their resistances add. Ideal parallel branches have the same node-to-node potential difference; reciprocal resistances add and branch currents sum at junctions. A parallel equivalent resistance is smaller than the smallest positive branch resistance. These introductory calculations assume ideal wires and a maintained ideal supply voltage. Real sources have internal resistance and protective limits; calculations do not substitute for electrical safety procedures.