Which statement best describes the total resistance in a parallel circuit?

Which statement best describes the total resistance in a parallel circuit?

• A. It is greater than the largest branch resistance.
• B. It is equal to the smallest resistance among branches.
• C. It is less than the smallest individual resistance in any branch.
• D. It is equal to the average resistance of all branches.

Answer: (C)

In a parallel circuit, the currents have multiple paths to flow, so the overall opposition to current is reduced. The total resistance is found using 1/R_total = 1/R1 + 1/R2 + ... . Because you’re adding positive reciprocals, the sum is larger than any single 1/R_i, which makes R_total smaller than the smallest branch resistance. For example, two 6-ohm resistors in parallel give 3 ohms, which is less than either 6-ohms branch. The only time you wouldn’t have R_total less than the smallest branch is if there is only one path (no parallel branches). So the total resistance in a parallel circuit is indeed less than the smallest individual resistance in any branch.

In a parallel circuit, the currents have multiple paths to flow, so the overall opposition to current is reduced. The total resistance is found using 1/R_total = 1/R1 + 1/R2 + ... . Because you’re adding positive reciprocals, the sum is larger than any single 1/R_i, which makes R_total smaller than the smallest branch resistance. For example, two 6-ohm resistors in parallel give 3 ohms, which is less than either 6-ohms branch. The only time you wouldn’t have R_total less than the smallest branch is if there is only one path (no parallel branches). So the total resistance in a parallel circuit is indeed less than the smallest individual resistance in any branch.