# Parallel Resistance Calculator

## Calculating Parallel Resistances

In a parallel circuit, two or more resistors share the same voltage source but have separate paths for current to flow. Unlike series resistances, where the total resistance is simply the sum of individual resistors, parallel resistors follow a different rule.
In parallel, the total resistance R_{total} is always less than the smallest individual resistance in the circuit.

Mathematically, this relationship is expressed as:

R_{total} = 1 / ( 1 / R_{1} + 1 / R_{2} + 1 / R_{3} + ... + 1 / R_{n} )

The reciprocal formula essentially encapsulates the concept that in parallel circuits, resistors with smaller values (lower resistance) allow more current to flow through them, and the formula calculates how the conductance of all these paths combines to provide a total conductance (inverse of resistance) for the entire parallel circuit.