What is the total resistance in a parallel circuit compared to the smallest resistance?

In a parallel circuit, the total resistance is always less than the smallest individual resistance among the resistors connected in parallel. This is a fundamental characteristic of parallel circuits, stemming from the fact that adding more paths for current to flow reduces the overall opposition to the flow of electricity.

When resistors are connected in parallel, the formula to calculate the total resistance (R_total) is given by:

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

This indicates that the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. As a result, since the reciprocal of the total resistance is a sum of fractions, where each fraction represents the reciprocal of an individual resistance, the total resistance will always be smaller than the smallest of those individual resistances.

For instance, if you have two resistors of 4 ohms and 6 ohms in parallel, the total resistance will be calculated as follows:

1 / R_total = 1 / 4 + 1 / 6

1 / R_total = 3/12 + 2/12 = 5/12

Thus, R_total = 12/5 =