Professional Insights: The 3 Pillars of Cable Sizing

Sizing an electrical cable is a critical engineering task that goes far beyond just "picking a wire that fits." A correctly sized cable operates safely and efficiently for decades, while an incorrectly sized one is a catastrophic fire and equipment-failure hazard. This tool analyzes the three fundamental pillars of cable selection: Ampacity, Voltage Drop, and Short-Circuit Withstand.

1. Ampacity: Protecting the Cable

What is it? Ampacity (a blend of "ampere" and "capacity") is the maximum current a cable can continuously carry without exceeding its insulation's temperature rating (e.g., 70°C for PVC, 90°C for XLPE). It is not a fixed number; it's a dynamic rating based on a simple principle: Heat In vs. Heat Out.

• Heat In: Generated by current flowing through the conductor's resistance (`I²R` losses).
• Heat Out: Dissipated from the cable surface into the surrounding environment.

The cable's ampacity is the point where "Heat In" equals "Heat Out." This is why we apply derating factors:

• Ambient Temperature ($$k_{temp}$$): A hotter day (e.g., 45°C) means the environment can absorb less heat. The cable can't dissipate as much, so its ampacity decreases.
• Grouping ($$k_{group}$$): Laying cables side-by-side means they heat each other. This "mutual heating" drastically reduces the "Heat Out" for every cable in the bundle, significantly lowering their ampacity.
• Burial ($$k_{soil}$$ & $$k_{depth}$$): Soil is a thermal insulator. "Damp" soil (low resistivity, e.g., 1.5 K·m/W) dissipates heat well. Dry, sandy soil (high resistivity, e.g., 3.0 K·m/W) traps heat, lowering ampacity. Burying a cable deeper also makes it harder for heat to reach the surface, further reducing its rating.

2. Voltage Drop: Protecting the Load

A cable can be safe (not exceeding its ampacity) but still be incorrect. As current flows through the cable's impedance (resistance R and reactance X), the voltage "drops" along its length. If a 400V motor is fed by a very long, undersized cable, it might only receive 370V.

This low voltage starves the motor, causing it to draw higher current to produce its required power. This leads to overheating, insulation damage, and premature failure of your expensive load (motor, pump, etc.). Standards like NEC/IEC recommend limiting voltage drop to 3-5% to ensure equipment health.

3. Short-Circuit Withstand: Protecting the System

This is the "emergency" scenario. Ampacity and voltage drop are for normal operation. Short-circuit withstand is about surviving a fault. When a fault occurs (e.g., a bolted short circuit), the current can instantly spike to 10,000A, 25,000A, or more.

The cable must be able to withstand this massive thermal and magnetic stress for the short time (e.g., 0.1 seconds) it takes the upstream circuit breaker to trip. This is calculated using the adiabatic formula $$I^2t = k^2S^2$$. If the cable is too small, it will be physically destroyed (vaporized) by the fault before the breaker can even act, turning a controllable fault into an unmitigated disaster.