What method is used to calculate total resistance in a parallel circuit with two resistors?

In a parallel circuit with two resistors, the total resistance is calculated using the product over sum method. When resistors are connected in parallel, the overall resistance decreases as more resistors are added to the circuit. This is because the resistors provide multiple pathways for the current to flow.

The formula for calculating the total resistance ( R_t ) in a parallel circuit with two resistors ( R_1 ) and ( R_2 ) is given by:

[

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

]

This formula reflects that the total resistance is a fraction where the numerator is the product of the two resistances and the denominator is the sum of the two resistances. This results in a value that is always less than the smallest individual resistance in the circuit, demonstrating the principle that parallel pathways for electrical flow can reduce overall resistance.

The other methods mentioned do not correctly represent how to calculate total resistance in a parallel configuration. The sum of resistances, for example, applies to series circuits, while the inverse of the sum is a conceptual misunderstanding for this context. The square of the sum does not apply and does not relate to resistance calculations in parallel