In a parallel circuit, total resistance is typically...

In a parallel circuit, total resistance is typically...

• A. Less than the smallest branch resistance.
• B. Equal to the sum of branch resistances.
• C. Greater than the largest branch resistance.
• D. Unrelated to branch values.

Answer: (A)

In parallel circuits, the same voltage drives each branch, but the current can split among many paths. This makes the total conductance the sum of the branch conductances, so 1/R_total = 1/R1 + 1/R2 + … . Since you’re adding positive numbers, 1/R_total is larger than any individual 1/Ri, which means R_total is smaller than any single branch resistance. That’s why the total resistance in a parallel network is typically less than the smallest branch resistance. For example, two 6-ohm resistors in parallel give 3 ohms. This isn’t equal to the sum (that would be a series case), and it’s not greater than the largest branch.

In parallel circuits, the same voltage drives each branch, but the current can split among many paths. This makes the total conductance the sum of the branch conductances, so 1/R_total = 1/R1 + 1/R2 + … . Since you’re adding positive numbers, 1/R_total is larger than any individual 1/Ri, which means R_total is smaller than any single branch resistance. That’s why the total resistance in a parallel network is typically less than the smallest branch resistance. For example, two 6-ohm resistors in parallel give 3 ohms. This isn’t equal to the sum (that would be a series case), and it’s not greater than the largest branch.