What happens to the total resistance in a parallel circuit as more branches are added?

In a parallel circuit, adding more branches provides additional pathways for current to flow. The total resistance in a parallel circuit is determined using the formula for parallel resistances, which is the reciprocal of the sum of the reciprocals of each individual resistance.

When additional branches with resistance are added, the total resistance decreases because each new path allows more current to flow. This means that the overall ability of the circuit to conduct electricity improves. Essentially, the equation for total resistance (R_total) in a parallel circuit can be expressed as:

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

As more branches (or resistors) are added, the left side of the equation becomes larger, leading to a smaller overall value for R_total. In practical terms, this is why resistance decreases: more conductive paths result in less overall opposition to the current flow.

Therefore, when examining how resistance changes with the addition of branches in a parallel circuit, it is clear that the total resistance decreases as more branches are added.