Resistors in Parallel & Series Calculator

Resistor Combinations Guide

Series Resistors

Series: resistors connected end-to-end in a single path. Same current through each. Voltage drops add up to total supply voltage. R_total = R₁ + R₂ + R₃ + ... + Rₙ. Current: I = V_supply / R_total. Voltage drop across each: V_i = I × R_i. Higher resistance = more voltage dropped. Applications: voltage dividers (specific resistor ratio for desired output voltage). Current-limiting in series with LEDs. Reducing voltage to logic level. Total power: P = V × I = V² / R_total. Distributed proportional

Parallel Resistors

Parallel: resistors connected between same two points. Same voltage across each. Currents through each add to total supply current. 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ. Equivalent formula for 2 resistors: R_total = (R₁ × R₂) / (R₁ + R₂). Key property: total resistance always LESS than smallest individual resistor. Two equal R in parallel = R/2. Three equal R in parallel = R/3. Approximation: very different values (10× ratio): R_total ≈ smaller resistor. Useful mental shortcut. Current th

Series-Parallel Networks

Combinations of series and parallel sections common in real circuits. Solve by reducing complex network step-by-step: 1. Find a section that's purely series OR purely parallel. 2. Replace with single equivalent resistor. 3. Repeat until network reduces to single resistor. 4. Calculate current. 5. Work back through original network finding individual currents/voltages. Voltage divider example: 5V supply, R1 = 1kΩ (top), R2 = 2.2kΩ (bottom). V_out across R2 = 5V × R2/(R1+R2) = 5 × 2.2/3.2 = 3.4V.

Practical Considerations

Component tolerances: standard ±5% (gold band) or ±1% (brown band). Real resistance varies. Calculated values are nominal. Critical circuits (voltage references, precision filters) require ±0.1% or matched-pair resistors. Power dissipation: each resistor has power rating. 1/4W (250mW) most common. Exceed power rating — resistor overheats, drifts, eventually fails. Check P = I²R or V²/R for each resistor. Common applications: voltage dividers for ADC inputs. Current sense resistors (very low valu