gen-define-series-versus-parallel-resistance-and-give-one-short-078d

Define series versus parallel resistance and give one short worked example.

# Series vs Parallel Resistance ## **Series Resistance** Resistors connected **end-to-end** in a single path where the same current flows through each resistor. **Formula:** R_total = R₁ + R₂ + R₃ + ... ## **Parallel Resistance** Resistors connected **across the same two points** where the voltage across each resistor is the same, but current divides among paths. **Formula:** 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... --- ## **Worked Example** **Problem:** Find the total resistance when: - Three 6Ω resistors are connected in series - Three 6Ω resistors are connected in parallel **Series Solution:** ``` R_total = R₁ + R₂ + R₃ R_total = 6Ω + 6Ω + 6Ω = 18Ω ``` **Parallel Solution:** ``` 1/R_total = 1/6 + 1/6 + 1/6 = 3/6 = 1/2 R_total = 2Ω ``` **Key Insight:** Series resistance *increases* total resistance, while parallel resistance *decreases* it (provides more paths for current flow).