In a parallel circuit, the resistance is always what in relation to the smallest resistor value?

In a parallel circuit, the overall resistance is always less than the smallest resistor value present in the circuit. This is due to the way resistors behave when connected in parallel. When multiple resistors are connected in parallel, the current has multiple paths to flow through, which decreases the total resistance of the circuit.

Mathematically, the total resistance ( R_{total} ) of parallel resistors can be found using the formula:

[

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots

]

When you have at least one resistor, this formula shows that the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. As a result, since adding more paths for the current effectively allows more current to flow, the total resistance decreases.

Furthermore, the smallest resistor in the circuit has the largest conductance (since conductance is the inverse of resistance), which will dominate the total conductance. Therefore, the total resistance cannot exceed the smallest resistor's value. This is why, in a parallel circuit, the overall resistance is always less than the