In a parallel circuit, what happens to the total resistance as more resistors are added?

In a parallel circuit, when more resistors are added, the total resistance decreases. This occurs because each additional resistor provides an alternative pathway for current to flow. In a parallel arrangement, the total current is the sum of the currents through each parallel branch, which effectively means that the total resistance is reduced.

The relationship governing this can be represented by the formula for total resistance in parallel circuits, given as:

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

As more resistors are added (R2, R3, etc.), the terms in the equation increase, resulting in a larger denominator when calculating R_total. Consequently, R_total becomes smaller, leading to a decrease in overall resistance. Therefore, adding resistors in parallel enhances current flow, lowers resistance, and enables the circuit to operate more efficiently.