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?
Correct Answer: increases
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:
Initial: 1 / R_eq(initial) = G1 + G2 + ... + Gn.Remove one: 1 / R_eq(new) = G1 + G2 + ... + G(n-1) < original sum.Thus R_eq(new) = 1 / (smaller sum) is larger → total resistance increases.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