What is the formula used to calculate total resistance in a parallel circuit?

The formula to calculate the total resistance in a parallel circuit is based on the principle that the total current flowing through the circuit is the sum of the currents through each parallel branch. In a parallel configuration, the voltage across all components remains the same, but the total current is divided among the various paths.

The correct formula, R_total = 1/(1/R1 + 1/R2 + ... + 1/Rn), reflects this relationship. When you use this formula, you effectively find the reciprocal of the total resistance by taking the sum of the reciprocals of each individual resistance. This makes sense physically because adding resistances in parallel decreases the overall resistance of the circuit; more paths allow more current to flow, reducing the total opposition to current.

Using this formula ensures an accurate calculation of total resistance in a circuit where components are configured in parallel, accommodating for the way current and voltage works in such a setup. It confirms that the total resistance will always be less than the smallest individual resistance among them.