Parallel Resistance

Resistors in Parallel

When resistors are connected side-by-side (in parallel), they share the same voltage. The total resistance is always less than the smallest individual resistor:

rac{1}{R_ ext{total}} = rac{1}{R_1} + rac{1}{R_2} + rac{1}{R_3} + cdots

Why?

Each parallel path gives current another route through the circuit. Adding a parallel resistor is like opening another lane on a highway — total throughput increases, so effective resistance decreases.

For Two Resistors

A useful shorthand: product over sum

R_ ext{total} = rac{R_1 R_2}{R_1 + R_2}

Examples

Your Task

Implement parallel_resistance(resistances) taking a list and returning the combined parallel resistance.