What is the formula for total resistance in a parallel circuit?

In a parallel circuit, the total resistance is determined by the reciprocal of the sum of the reciprocals of each resistor's resistance value. This relationship arises because, in parallel configurations, the voltage across each resistor is the same, while the total current is divided among the various paths provided by each resistor.

The formula 1/R_total = 1/R1 + 1/R2 + 1/R3 accurately reflects how total resistance is calculated in such a circuit. Each resistor provides an alternative path for current to flow, leading to a decrease in the total resistance as more parallel paths are added. Therefore, the inverse relationship encapsulated in this formula showcases that as individual resistances decrease, the overall total resistance also decreases.

The other options do not correctly represent how resistance behaves in parallel circuits. The first option simply adds the resistances together, which applies to series circuits. The second option misapplies the addition of resistance in terms of reciprocals, while the fourth option incorrectly describes the product of resistances, which again only applies to series circuits, rather than parallel scenarios.