Resistors in Parallel

When several resistors are connected between the same two points, they're said to be joined in parallel. Unlike series, every resistor here sees the same potential difference — the one across the shared pair of points — which you can check by placing a voltmeter across each resistor individually.

The current, though, splits between the branches. If I₁, I₂, and I₃ are the currents through three parallel resistors, the total current drawn from the battery is their sum: I = I₁ + I₂ + I₃.

Applying Ohm's law to the combination (I = V/Rp) and to each resistor (I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃), and substituting into I = I₁ + I₂ + I₃, gives V/Rp = V/R₁ + V/R₂ + V/R₃. Since V cancels, 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ — the reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances. This always makes Rp *smaller* than the smallest individual resistance.

Parallel circuits solve both problems series circuits have: each appliance gets the full voltage and draws exactly the current it needs (a bulb and a heater can coexist happily), and if one component fails, the others keep working — which is exactly how household wiring is done.