In a parallel circuit, how does the total resistance compare to the resistances of the individual resistors?

In a parallel circuit, the total resistance is determined by the arrangement of resistors such that the current has multiple paths to flow through. The key principle in parallel circuits is that total resistance is always less than the resistance of the smallest individual resistor within that circuit. This can be attributed to the fact that each additional resistor provides an alternative path for the current, effectively reducing the overall resistance against the flow.

When calculating total resistance in a parallel configuration, the reciprocal formula is used:

1/R_total = 1/R_1 + 1/R_2 + ... + 1/R_n.

According to this equation, adding more resistors decreases the total resistance. Since the lowest individual resistance contributes to lowering the total resistance significantly, the total resistance cannot exceed or be equal to that of the smallest resistor—it will always be lower. The implication is that as more resistors are added in parallel, the total resistance continues to decrease, moving further below the smallest resistor's resistance value. Therefore, the relationship stands that the total resistance is indeed less than the smallest resistor in the circuit.