In a parallel circuit, what is the relationship between total resistance and the individual branches?

In a parallel circuit, the total resistance is indeed less than that of the individual branches. This occurs because each branch offers a separate path for the current to flow. When more branches are added to the circuit, the overall current can increase, while the voltage across each branch remains constant, according to Ohm's Law.

The formula for calculating the total resistance in a parallel circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances. Mathematically, this can be represented as:

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

This relationship shows that adding more branches (with their respective resistances) results in a decrease in total resistance. Consequently, the total resistance will always be less than the smallest individual resistance in any branch.

Understanding this principle is crucial for analyzing and designing circuits, as it underlies the behavior of electrical systems where multiple components function simultaneously while sharing voltage and allowing for an increased total current.