Parallela

Meet Parallela, two resistors side by side who offer the current more than one way through.

When resistors are connected in parallel, each one sits directly across the same voltage, and the current splits between them. Adding another path lets more total current flow for the same voltage, so the combined resistance is lower than either branch alone. The rule follows from Ohm's law and charge conservation: 1/R = 1/R₁ + 1/R₂.

Two equal 100 Ω resistors give 1/R = 1/100 + 1/100 = 2/100, so R = 50 Ω, half of one. A 100 Ω and a 220 Ω together give R = 1 / (1/100 + 1/220) ≈ 68.75 Ω, less than the smaller one.

Household circuits are wired in parallel, so every appliance gets the full supply voltage and can be switched on and off independently.

A caution: every extra parallel load lowers the total resistance and raises the total current, which is why too many appliances on one circuit can overload it and trip a breaker. Real wires also add a little resistance of their own.