Fault behavior in parallel networks — if one branch opens, does the total (equivalent) resistance decrease?

Introduction / Context:Understanding how faults affect equivalent resistance is key to troubleshooting. An open circuit in one branch of a parallel network removes that path entirely. This item asks whether the overall resistance goes down or up when a branch opens.

Given Data / Assumptions:

• Several resistors connected in parallel across a source.
• One branch becomes open (infinite resistance), eliminating its conductance contribution.
• Source voltage remains constant and other branches are unaffected.

Concept / Approach:Parallel equivalent resistance is governed by conductance addition: G_eq = Σ (1/Rk). Opening a branch sets 1/R_open = 0, removing that term. Therefore total conductance decreases, and equivalently, total resistance Req = 1/G_eq increases. With higher Req at a fixed voltage, total current drawn from the source decreases. Hence, the statement that total resistance decreases is incorrect; it increases.

Step-by-Step Solution:

Verification / Alternative check:Example: R1 = R2 = 10 Ω in parallel → Req = 5 Ω. Open R2 → only R1 remains → Req = 10 Ω, which is larger, not smaller.

Why Other Options Are Wrong:

• Answering “True” would imply that removing a current path somehow lowers resistance, contradicting the physics of fewer available conduction paths.

Common Pitfalls:Confusing series and parallel responses to opens: an open in series breaks the circuit and sends resistance to infinity; an open in one parallel branch simply removes that branch while leaving other paths intact but increasing overall resistance.

Final Answer:False