Final answer:
In a parallel circuit, the equivalent resistance decreases because there are more paths for the current to flow, thus lowering the total resistance below that of the smallest resistor in the network.
Step-by-step explanation:
The equivalent resistance of a parallel combination of resistors is always less than the smallest of these resistors because of the way currents divide in a parallel circuit. When resistors are added in parallel, there are more paths for the current to take, which in turn decreases the overall resistance of the combination. This is because with each additional path, more current can flow from the source to the resistors, reducing the total resistance (total resistance Rp) compared to what the resistance would be through any single resistor.
For example, imagine water flowing through a set of parallel pipes; the more pipes there are, the easier it is for water to flow, which is similar to electrical current in parallel resistors. Therefore, this relationship inevitably results in a total resistance that is less than the smallest individual resistance in the parallel network.
When tackling a complex network of resistors, which includes both series and parallel configurations, resistors can be systematically reduced to a single equivalent resistance. It may be time consuming, but it isn't particularly difficult to do.