Parallel Circuits

A parallel circuit contains two or more conducting branches connected between the same pair of points. Charge can therefore travel through different paths.

The potential difference across each parallel branch is the same: **V = V₁ = V₂ = V₃**

At a junction, current divides among the branches. The total current is: **Iₜ = I₁ + I₂ + I₃** The currents recombine when the branches join again.

For resistors in parallel: **1Rₜ = 1R₁ + 1R₂ + 1R₃ + ... The equivalent resistance of a parallel combination is less than the smallest individual branch resistance**.

Two resistors, 6 Ω and 3 Ω, are in parallel. `1Rₜ = 16 + 13` `1Rₜ = 16 + 26 = 36` `1Rₜ = 12` **Rₜ = 2 Ω**

Different branches can operate independently. If one branch opens, other complete branches may continue operating. This is one reason household appliances are connected in parallel rather than as one long series chain.