Series and Parallel Circuits

Objective: Calculate current, voltage division, and equivalent resistance.

A series circuit has a single path through its components. In steady conditions the same current passes every element; potential differences across loads add to the source potential difference around a loop. For ohmic resistors, R_eq = R₁ + R₂ + … . A 2 Ω and 4 Ω series pair connected to an ideal 12 V source has 6 Ω equivalent resistance and 2 A current; the voltage drops are 4 V and 8 V. Opening the only path stops current through the entire circuit. These relations assume wires with negligible resistance and a source appropriately modeled as ideal; real devices may differ.

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: Use P = IV and distinguish ideal predictions from real limits.

Electrical power delivered to a component is P = IV under the passive sign convention, with watt as the unit. For an ohmic resistor, P = I²R = V²/R; a 12 V, 3 A device receives 36 W. Energy delivered over constant power for duration t is E = Pt. A short circuit provides a low-resistance path and can draw excessive current from a real source, whose internal limits and protective devices matter. Ideal circuit diagrams omit wire resistance, heating, and source behavior; do not infer that every battery can deliver arbitrary current. Circuit calculations should name the component, current, voltage, and assumptions.