Series & Parallel Resistance Calculator

Resistors in series and parallel

In series, resistances add: Rtotal = R₁ + R₂ + … + Rₙ. In parallel, reciprocals add: 1/Rtotal = 1/R₁ + 1/R₂ + … + 1/Rₙ. For two resistors in parallel, the shortcut is R = (R₁ · R₂) / (R₁ + R₂). Series shares the same current; parallel shares the same voltage. Mind the units (Ω, kΩ, MΩ). Kirchhoff's voltage law (KVL) states that the sum of voltages around any loop equals zero — that's why series voltages add up to the source. Complex circuits reduce by series/parallel blocks; when that fails, use Thévenin/Norton, mesh, nodal, or superposition analysis. Example: 100 Ω and 200 Ω in series = 300 Ω; the same pair in parallel = (100·200)/300 ≈ 66.7 Ω.

Applications: wiring, voltage dividers and grounding

Use series/parallel reduction to size copper wires per Brazilian standard NBR 5410, design multi-stage voltage dividers, build dummy loads (guitar amplifier testing), and engineer grounding systems where multiple electrodes in parallel lower the ground resistance below 10 Ω. It's also fundamental to LED arrays, current-sensing shunts, and impedance matching in audio circuits.

FAQ

Why is parallel resistance always smaller than the smallest resistor? Adding paths gives current more options to flow — total opposition drops.

What if I parallel two equal resistors? The result is half the value. Three equal in parallel = one-third. N equal in parallel = R/N.

What about power dissipation? Each resistor dissipates P = V² / R (its own voltage). In series, the largest R dissipates the most power; in parallel, the smallest R does.

When does the series/parallel method fail? Bridge circuits (e.g., Wheatstone bridge) and circuits with multiple sources usually need mesh or nodal analysis — pure reduction won't simplify them.