Resistor value vs. wattage — is a resistor’s numeric resistance (in ohms) directly proportional to its power handling capability (watt rating), or are these independent specifications?

Introduction / Context:
Resistor datasheets list at least two fundamentally different specifications: resistance value (ohms) and power rating (watts). Confusing these leads to poor part selection and overheating in products. The question probes whether the two are directly proportional, which they are not.

Given Data / Assumptions:

• Commercial resistors with specified ohmic values and watt ratings.
• Ambient conditions and mounting affect derating but do not couple ohms to watts mathematically.
• Thermal design governs power rating via size and materials.

Concept / Approach:
Resistance is set by material resistivity, geometry, and construction; power rating is set by how much heat the body can dissipate while staying within safe temperature rise. You can buy a 10 Ω resistor rated at 1/4 W or 10 W; the ohmic value does not force a specific watt rating. Conversely, two resistors of the same wattage can have wildly different resistances.

Step-by-Step Solution:

Verification / Alternative check:
Compare catalog parts: the same 1 kΩ value is offered in 1/8 W, 1/4 W, 1/2 W, 1 W, etc., illustrating independence of specs.

Why Other Options Are Wrong:

• “Higher ohms → higher watt”: demonstrably false from catalogs.
• “Only for wirewound” or “because P = I^2 * R”: the equation gives operating power, not rated power; construction sets rating.
• “Indeterminate without tolerance/TC”: those are separate parameters.

Common Pitfalls:
Assuming higher resistance dissipates more heat; in fact, dissipation depends on the applied V or I and the environment.

Final Answer:
Incorrect — resistance and watt rating are independent specifications.