Which of the following conditions would most likely lead to the failure of a resistor due to overheating?

Correct Answer: Option A — Resistor wattage rating one half that required for the circuit.

Operating a resistor with a wattage rating half of what the circuit requires causes excessive thermal dissipation relative to its surface area, leading to rapid overheating, carbonization, and catastrophic failure. Resistors must be rated equal to or greater than calculated circuit power per IEEE 45.