What type of circuit arrangement has a total resistance that is always less than the smallest resistor value?

In a parallel circuit arrangement, the total resistance is indeed always less than the smallest resistor value present in the circuit. This occurs because in a parallel circuit, there are multiple paths for current to flow. Each added resistor provides an alternative pathway for current, which effectively decreases the overall resistance of the circuit.

The mathematical relationship for total resistance in a parallel circuit can be described by the formula:

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

This means that adding more resistors in parallel will result in a total resistance that approaches zero as the number of resistors increases. Consequently, the total resistance will always be lower than the smallest individual resistor in the network.

In summary, the nature of parallel circuits facilitates a significant reduction in overall resistance as multiple pathways for current exist, thus ensuring that the total resistance is less than that of the smallest resistor.