Effect of removing a branch: If one resistor is taken out of a parallel circuit and the remaining network is reconnected, what happens to the total resistance seen by the source?

Introduction / Context:
Understanding how total resistance changes with the number of parallel paths is essential for predicting current draw and power. Removing a branch changes the equivalent resistance and thus the load on the source.

Given Data / Assumptions:

• A parallel network initially has multiple resistive branches.
• One resistor is removed (opened) and the circuit is restored without that branch.
• All other components and source voltage remain unchanged.

Concept / Approach:
For resistors in parallel: 1 / R_eq = Σ (1 / R_i). Removing a branch eliminates a positive term from the sum of conductances, so the total conductance decreases. Therefore, R_eq = 1 / (Σ conductance) increases.

Step-by-Step Reasoning:

Verification / Alternative check:
Numerical example: two 100 Ω in parallel → R_eq = 50 Ω. Remove one branch → R_eq = 100 Ω, which is larger than 50 Ω.

Why Other Options Are Wrong:

• Decreases: Opposite of parallel behavior when removing paths.
• Remains the same / doubles: Not generally true; change depends on values and count, but resistance definitely increases.

Common Pitfalls:

• Confusing series and parallel rules; in series, removing a resistor can decrease total resistance, but not in parallel.

Final Answer:
increases