In a parallel circuit, what happens to the total resistance?

In a parallel circuit, the total resistance decreases as more components are added. This is because each additional branch provides an alternative path for the current, effectively allowing more current to flow through the circuit. The formula for calculating total resistance in a parallel setup is derived from the reciprocal of the sum of the reciprocals of the individual resistances. Mathematically, this is expressed as:

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

When additional resistors are added in parallel, the total resistance becomes less than the smallest resistance in the circuit. This reduction in resistance occurs because the pathways for current to flow increase with each additional branch, thus reducing the overall resistance encountered by the current.

In contrast, in a series circuit, adding more resistors would increase the total resistance, which is not the case here. The total resistance does not stay the same or fluctuate based on voltage; rather, it is dependent on the configuration of the circuit and the resistors involved.