What happens to the total resistance in a parallel circuit?

In a parallel circuit, adding more branches actually decreases the total resistance. This occurs because each added branch provides an additional pathway for current to flow. When there are multiple paths, the overall ability of the circuit to conduct electricity increases, which results in a lower total resistance.

The total resistance in a parallel circuit can be calculated using the formula (1/R_{total} = 1/R_1 + 1/R_2 + 1/R_3 + \ldots). This formula illustrates that as more resistive branches are added, the value of (1/R_{total}) increases, causing (R_{total}) to decrease. Hence, the more branches you add, the total resistance goes down, facilitating a larger amount of current to flow through the circuit for the same voltage.

In contrast, if resistance were to increase with additional branches, it would imply that adding pathways for current would hinder the flow, which contradicts the fundamental principles of how parallel circuits operate. Keeping the resistance constant would mean that no additional branches could affect the overall flow, which is not the case in a parallel configuration. Additionally, stating that total resistance equals the sum of individual resistances applies to series circuits, where the resistors are arranged in a