What is true about the total resistance of a parallel circuit?

In a parallel circuit, the total resistance is always less than the smallest individual resistance in the circuit. This occurs because, in a parallel configuration, each resistor provides an alternative pathway for the current. As more resistors are added in parallel, the overall ability of the circuit to conduct current increases, which reduces total resistance.

The relationship can be understood through the formula for total resistance (R_total) in a parallel circuit, which is given by:

1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

This equation illustrates that the sum of the reciprocals of each resistance leads to a total that results in a lower value than any single resistor's resistance. Thus, as the number of pathways increases, the overall resistance of the circuit decreases, validating that the total resistance is indeed less than the smallest resistor in the configuration.

This principle is fundamental in electrical circuit design and analysis, especially when considering efficiency and current distribution among various components.