Effect of removing one branch: Five identical 100 Ω resistors are in parallel. If one resistor is removed (open-circuited), what is the new total resistance?

Introduction / Context:Uniform parallel branches make mental math fast. Knowing how total resistance changes when branches are added or removed is essential for troubleshooting and quick hand calculations in the lab.

Given Data / Assumptions:

• Five equal resistors: each 100 Ω.
• Original configuration: all five in parallel.
• One branch is removed; four equal branches remain in parallel.

Concept / Approach:

For N equal resistors of value R in parallel, the equivalent resistance is R_eq = R / N. This comes from 1 / R_eq = N / R. When one branch is removed, simply reduce N accordingly and recompute.

Step-by-Step Solution:

Verification / Alternative check:

Using conductances: each branch has conductance 1/100 = 0.01 S. Four branches give 0.04 S total, hence R = 1/0.04 = 25 Ω, matching the quick formula.

Why Other Options Are Wrong:

20 Ω is the five-branch case, not four. 500 Ω and 100 Ω contradict the rule that parallel R must be less than any single branch. 50 Ω does not match R/N with N = 4.

Common Pitfalls:

Accidentally using series addition or forgetting that removing a branch increases the total resistance (fewer current paths).

Final Answer:

25 Ω