What can be said about the total resistance of a parallel circuit?

In a parallel circuit, the total resistance is always less than the smallest resistance present in that circuit. This characteristic arises from how resistances combine in a parallel configuration. When resistors are connected in parallel, the total current is divided among the various paths, allowing a greater total current to flow than would be possible through any single resistor alone.

The formula for total resistance in a parallel circuit can be expressed as:

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

From this formula, it becomes clear that adding resistors in parallel introduces additional pathways for current, effectively reducing the total resistance. The total resistance does not simply equal the smallest resistance because the interaction between the resistors allows for a decrease as more are added.

In practical terms, when considering resistances in parallel, the presence of even one small resistor will dominate the effect on the total resistance, ensuring that it remains less than the smallest of all the resistors in the circuit. This principle is fundamental in electrical engineering, particularly in applications where controlling current flow is essential.