Open-circuit fault effect between A and B — suppose nodes A and B are connected only through a single resistor R3 (no alternate paths). If R3 fails open, what is the resulting total resistance RT measured between A and B?

Introduction / Context:An open-circuit failure removes a current path. When there is only a single conduction path between two nodes, opening that element isolates the nodes and makes the equivalent resistance between them unbounded (infinite). Recognizing this outcome is vital for fault analysis and troubleshooting.

Given Data / Assumptions:

• Nodes A and B are connected solely through resistor R3.
• No other series or parallel paths exist between A and B.
• R3 fails open (break in continuity).

Concept / Approach:Resistance between two nodes is defined as the ratio V/I under a small test stimulus. If there is no conductive path, any finite applied voltage produces zero current, so R = V / I → ∞. Therefore, the equivalent resistance becomes infinite when the only branch is open. This is independent of the original resistance value of R3 prior to failure.

Step-by-Step Solution:

Verification / Alternative check:In measurement, an ohmmeter shows “OL” or very large resistance when probes are placed across A and B after the open occurs. Circuit simulators report no DC path between the nodes.

Why Other Options Are Wrong:

Common Pitfalls:Assuming other leakage paths exist (they do not in this idealized scenario); confusing “large” with “infinite” — in analysis, we model an ideal open as infinite resistance.

Final Answer:Infinite resistance