In a parallel combination of resistors, if one branch is removed, what happens to the equivalent resistance?

• A. It decreases
• B. It stays the same
• C. It increases
• D. It becomes zero

Answer: (C)

In a parallel network, each branch adds another path for current, so the overall conductance (the sum of 1/R for each branch) increases as you add branches. The equivalent resistance is the reciprocal of that total conductance: Req = 1/(1/R1 + 1/R2 + ...). When one branch is removed, you subtract its conductance from the total, so the sum gets smaller and Req gets larger. For example, two equal resistors R in parallel give Req = R/2. If you remove one branch, you’re left with just R, which is larger than R/2. So the equivalent resistance increases. It doesn’t decrease or stay the same, and it won’t become zero unless a short circuit appears across all branches.