In a parallel circuit, the total resistance is _______ the smallest resistance.

In a parallel circuit, the total resistance is less than the smallest resistance present in the circuit because of the way resistors divide the current. Each resistor provides an alternative path for the current, which means that the total current flowing through the circuit increases as more resistors are added in parallel. This leads to a decrease in the overall resistance of the circuit.

When resistors are connected in parallel, the formula for calculating total resistance (R_total) is given by the reciprocal of the sum of the reciprocals of the individual resistances. Mathematically, it can be expressed as:

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

From this relationship, it is evident that adding more resistors (each having a positive resistance value) will result in a lower total resistance than any individual resistor in the circuit. Consequently, the total resistance always ends up being less than the smallest resistor in a parallel configuration. This fundamental property of parallel circuits is essential for understanding circuit design and behavior.