In a parallel circuit, the total resistance will always be less than which of the following?

In a parallel circuit, the total resistance is calculated using the formula that takes into account the reciprocal of the individual resistances. This results in a total resistance that is always less than the resistance of the smallest resistor in the circuit.

The reason for this is that when resistors are connected in parallel, the electrical paths they create allow multiple paths for current to flow. The total resistance decreases as more branches are added because each additional path provides more options for current flow, effectively reducing the overall opposition to current. Thus, since the smallest resistance has the least opposition, it sets the lower limit for the total resistance; the total resistance cannot exceed this value.

In contrast, the largest resistance represents the highest level of opposition among the resistors and does not influence the overall reduction in resistance caused by the additional parallel paths. The average resistance of the circuit is also influenced by all resistors and does not set a limit on the total resistance in the same manner as the smallest resistor. Therefore, it is the smallest resistance that determines the threshold below which the total resistance will always fall in a parallel circuit.