Current, resistance, series and parallel

In a parallel connection every resistor is joined between the same two points, so the same voltage is across each branch. The charge can choose between the branches, so the branch currents add up to the total current: I = I₁ + I₂ + I₃. Each branch obeys I = V ÷ R, and this gives the rule for the equivalent resistance: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃. For two resistors it can be written R = R₁R₂ ÷ (R₁ + R₂), and for N equal resistors of r each, R = r ÷ N. Every new branch gives the charge one more path, so the equivalent resistance is smaller than the smallest resistor, and the branch with the smallest resistance carries the largest current. Solve in this order: find R, find the total current V ÷ R, find the branch currents V ÷ R₁ and so on, and check that they add up to the total.