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

In a parallel circuit, the total resistance decreases as more resistors are added. This occurs because each additional resistor provides an alternative pathway for current to flow, thereby increasing the overall capacity of the circuit to conduct electricity.

The fundamental principle governing this behavior is that when resistors are connected in parallel, the total resistance can be calculated using the formula:

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

From this formula, you can observe that adding more resistors to the circuit increases the number of pathways for current. As the number of pathways increases, the equivalent or total resistance decreases. Therefore, with a higher number of resistors in a parallel configuration, the total resistance approaches zero but never becomes zero unless an ideal conductor (like a superconducting wire) is introduced.

This principle is essential in circuit design, especially in applications where a low total resistance is desired for efficient current flow.