Parallel Resistance, Explained

When resistors are wired side by side, current can flow through each branch independently. The combined resistance follows the reciprocal rule: 1/Rt = 1/R1 + 1/R2 + 1/R3 + …. Each term 1/R is the conductance — how easily a branch lets current through — and the total conductance is simply their sum.

The Result Is Always Smaller

Because every added branch provides a new path for current, the total resistance of parallel resistors is always less than the smallest individual resistor. Two 100 Ω resistors in parallel make 50 Ω; four 100 Ω resistors make 25 Ω. This is why connecting speakers in parallel lowers the load impedance an amplifier sees.

Branch Currents

In a parallel circuit every resistor sees the full supply voltage, so each branch draws V/Rᵢ amps. The total current is the sum of the branch currents — the practical form of Ohm's law for parallel networks, and the reason fuses protect each circuit independently in household wiring.