Cable ampacity basics: The current-carrying rating of an insulated power cable primarily depends on which physical parameter(s)?

Introduction / Context:
Cable current rating (ampacity) is the maximum continuous current a cable can carry without exceeding its temperature limit. This rating is governed by heat generation (I^2 * R) and heat dissipation to the surroundings through the insulation and sheath. The question probes which geometric property most directly affects ampacity in basic terms.

Given Data / Assumptions:

• Comparing fundamental geometric effects (length vs. diameter) on current rating.
• Installation and environmental conditions are considered fixed.
• Steady-state thermal balance (no transients).

Concept / Approach:

For a given material and insulation system, conductor cross-sectional area (which scales with diameter for round conductors) determines resistance per unit length and the heat generated at a given current. Larger diameter (greater area) lowers resistance, reduces I^2 * R losses per unit length, and increases permissible current before reaching the temperature limit. Cable length does not directly change ampacity; it changes total voltage drop and total heat but not the allowable current per unit length that meets temperature constraints under uniform conditions.

Step-by-Step Solution:

Verification / Alternative check:

Thermal circuit models show conductor temperature rise ΔT ∝ (I^2 * r) / G_th, where G_th is thermal conductance to ambient per unit length. Increasing diameter reduces r and usually increases G_th slightly, improving rating.

Why Other Options Are Wrong:

• Length: does not set the allowable current; it affects voltage drop and total heating, not the fundamental ampacity.
• Both length and diameter: overstates the role of length in defining rating.
• None/ambient only: geometry (diameter/area) is essential.

Common Pitfalls:

• Confusing voltage-drop limits (length matters) with thermal ampacity (dominated by cross-section and installation conditions).

Final Answer:

diameter of cable