In a parallel circuit, how does the total resistance compare to the individual resistances?

In a parallel circuit, the total resistance is always less than the smallest individual resistance in the circuit. This is due to the way resistors are configured in parallel: each resistor provides an alternative pathway for current to flow. When multiple paths are available, the overall resistance to the flow of electricity decreases.

The relationship governing this is expressed by the formula for total resistance in a parallel circuit:

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

From this formula, it can be observed that as more resistors are added in parallel, the total resistance decreases because the reciprocal of the resistances adds together. Since adding pathways for current reduces the overall opposition to the current, the total resistance can never exceed the smallest individual resistance; instead, it always falls below that value.

Therefore, in a parallel circuit, the total resistance will invariably be less than the smallest individual resistance among the options available. This characteristic is fundamental to parallel circuits and is crucial for understanding their behavior in electrical systems.