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

In a parallel circuit, the total resistance is calculated using the reciprocal formula. The reason the correct equation states that the inverse of the total resistance (1/R_total) is equal to the sum of the inverses of each individual resistor (1/R1 + 1/R2 + 1/R3) is because when resistors are connected in parallel, the current can flow through multiple paths.

This configuration allows each resistor to share the total current, which decreases the overall resistance of the circuit. The more pathways available for the current, the less resistance the circuit has, which is effectively captured by adding the reciprocal values of the individual resistances. This results in a lower total resistance compared to any of the individual resistors.

Understanding this relationship is essential in analyzing electrical circuits, as it reflects how parallel connections amplify the capability of the circuit to carry current more efficiently.