What is true about the total resistance in a parallel circuit?

In a parallel circuit, the total resistance is uniquely calculated using the product-over-sum method because it accounts for the reciprocal nature of the resistances in parallel. When multiple resistors are connected in parallel, the total resistance can be determined by taking the reciprocal of the sum of the reciprocals of each individual resistance. This method effectively shows how the pathways provide multiple routes for current flow, which lowers the overall resistance of the circuit.

The product-over-sum method specifically refers to this calculation, where, for two resistors ( R_1 ) and ( R_2 ), the total resistance ( R_t ) can be computed as:

[

\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2}

]

In performing this calculation, you can end up with a total resistance that is lower than the smallest individual resistor in the parallel network due to the increased pathways available for current. This reinforces the understanding of parallel circuits, where the ability to take multiple paths drastically reduces resistance compared to series circuits. Thus, the product-over-sum method is the correct and most efficient way to calculate the total resistance in a parallel configuration.