When resistors are connected in parallel, how is the total resistance affected?

When resistors are connected in parallel, the total resistance decreases. This is a fundamental principle of electrical circuits. The reasoning behind this is based on the way the current flows through parallel resistors. Each resistor provides an alternative pathway for the current; thus, the more resistors you add in parallel, the easier it is for the current to flow.

Mathematically, the total resistance (R_total) in a parallel circuit can be calculated using the formula:

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

where R1, R2, R3, ..., Rn are the resistances of the individual resistors. Because you are adding the reciprocals of the resistances, the total resistance will always be lower than that of the smallest individual resistor in the group.

This makes parallel connections particularly useful when you want to reduce the overall resistance in a circuit, allowing for a larger current to flow. In contrast, connecting resistors in series would increase the total resistance, as the resistances simply add up, and a parallel configuration is specifically designed to lower resistance and increase circuit efficiency.