Three resistors of 10Ω, 20Ω, and 30Ω are connected in series. What is the total resistance?

In a series circuit, total resistance = sum of individual resistances. R_total = 10 + 20 + 30 = 60Ω. Series circuit characteristics: (1) Only ONE PATH for current; (2) Same current through every component; (3) Voltage divides among components (V_total = V₁ + V₂ + V₃); (4) Total resistance = sum of resistances; (5) Failure of one component (e.g., one bulb burning out) breaks the entire circuit; (6) Adding more components increases total resistance, reducing current. Classic example: old Christmas lights — series-wired, one bulb burns out, all go dark. Modern lights are usually parallel. Voltage divider: a common application of series resistors. Two resistors R₁ and R₂ in series across a voltage source V_in. The voltage across R₂ = V_in × R₂/(R₁ + R₂). This 'divides' the voltage proportionally — useful for getting a specific intermediate voltage from a power source. Example: 12V source with R₁ = 1000Ω and R₂ = 2000Ω. Voltage across R₂ = 12 × 2000/3000 = 8V. PARALLEL circuit by contrast: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ = 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60 = 11/60. R_total = 60/11 ≈ 5.45Ω. Note this is LESS than the smallest single resistor (10Ω) — that's always true for parallel. ASVAB EI tests both calculations and conceptual differences between series and parallel.