Cable ampacity basics: The current-carrying rating of an insulated power cable primarily depends on which physical parameter(s)?
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Alength of cable
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Bdiameter of cable
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Cboth length and diameter of cable
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Dnone of the above
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Eambient temperature only
Answer
Correct Answer: diameter of cable
Explanation
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:
Relate resistance per unit length r ∝ 1/Area; Area ∝ diameter^2.Heat generation per unit length q = I^2 * r → decreases with larger diameter.For fixed thermal environment, higher diameter permits higher I before insulation limit is reached.Length affects total drop (ΔV = I * r * L) but not the per-unit-length thermal limit that defines ampacity.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