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 the current to flow. When resistors are connected in parallel, the overall conductivity of the circuit increases, allowing more current to pass through.

The formula for calculating total resistance (R_total) in a parallel circuit is given by:

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

As you add more resistors (R2, R3, etc.), the sum of the reciprocals of their resistances increases. Consequently, this leads to a decrease in the total resistance. In fact, the total resistance will always be less than the smallest individual resistor in the parallel network. Thus, as resistors are added in parallel, the ability of the circuit to conduct electricity improves, supporting the idea that total resistance decreases with the addition of resistors.