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

In a parallel circuit, adding more branches actually decreases the overall resistance. This occurs because, in a parallel configuration, each additional branch provides an alternative path for the current to flow.

When resistors are connected in parallel, the total current supplied by the source increases as more pathways are available for the current, which means each individual pathway carries less current compared to when fewer branches are present. The overall resistance can be determined using the formula for total resistance in a parallel circuit, which is given by:

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

As more resistors (or branches) are added to this equation, the right-hand side becomes larger, resulting in a smaller value for R_total. Consequently, the overall resistance decreases. Therefore, the correct answer indicates the natural behavior of resistance in a parallel arrangement when more branches are introduced.