In a parallel circuit, the total resistance is always less than the smallest branch resistance. Which option is true?

In a parallel circuit, the total resistance is always less than the smallest branch resistance. Which option is true?

• A. False
• B. It depends
• C. It can be greater
• D. True

Answer: (D)

In a parallel circuit, adding more paths for current reduces the total resistance. The equivalent resistance is given by R_eq = 1 / (1/R1 + 1/R2 + ...). Because you’re summing positive reciprocals, the total 1/R_eq is larger than any single 1/Ri, so R_eq is smaller than any individual branch resistance. Therefore, with multiple finite branches, the total resistance is strictly less than the smallest branch resistance. The only exception is if all but one branch are open (infinite resistance), in which case the total equals that single finite branch and is not less. In typical multi-branch, finite-resistance parallel networks, the statement is true.

In a parallel circuit, adding more paths for current reduces the total resistance. The equivalent resistance is given by R_eq = 1 / (1/R1 + 1/R2 + ...). Because you’re summing positive reciprocals, the total 1/R_eq is larger than any single 1/Ri, so R_eq is smaller than any individual branch resistance. Therefore, with multiple finite branches, the total resistance is strictly less than the smallest branch resistance. The only exception is if all but one branch are open (infinite resistance), in which case the total equals that single finite branch and is not less. In typical multi-branch, finite-resistance parallel networks, the statement is true.