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

In a parallel circuit, the way total resistance is calculated leads to the principle that the total resistance is always less than the resistance of any individual branch. This occurs because in parallel circuits, each branch provides an alternative pathway for current to flow. When more pathways (or branches) are introduced, the total effective resistance decreases.

The formula for calculating total resistance in a parallel circuit involves taking the reciprocal of the sum of the reciprocals of each individual branch resistance. This can be summarized as:

1 / R_total = 1 / R_1 + 1 / R_2 + 1 / R_3 + ...

When you take this into account, the total resistance is effectively reduced by having multiple branches compared to any single branch resistance. This allows more current to flow than through any one branch alone, thus emphasizing that the total resistance must be less than the smallest individual resistance in the circuit.

In contrast, the other options do not accurately reflect the nature of resistance in parallel circuits. The total resistance cannot be greater than the greatest branch resistance, nor can it simply depend on the highest branch resistance or equal the average of all branch resistances. Instead, the total resistance will always be a composite value, lower than the resistance of the lowest branch,