Wire Overload Heat Calculator
Calculates the heat generated (power dissipation) in a wire during overload conditions, the temperature rise above ambient, and the time to reach a critical temperature using I²R heating principles.
Formulas Used
Wire Resistance from material properties:
R = ρ × L / A
Joule Heating Power (W):
P = I² × R
Heat Energy Generated (J):
Q = P × t = I² × R × t
Temperature Rise (°C) — adiabatic assumption:
ΔT = Q / (m × c) = (I² × R × t) / (m × c)
Time to Reach Critical Temperature (s):
tcrit = (m × c × (Tmax − Tamb)) / (I² × R)
Current Density (A/mm²):
J = I / A
Where: ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²), I = current (A), R = resistance (Ω), t = time (s), m = mass (kg), c = specific heat capacity (J/kg·K).
Assumptions & References
- Adiabatic model: All heat generated is absorbed by the wire itself — no heat loss to surroundings. This is conservative and valid for short overload durations (seconds to tens of seconds).
- Uniform current distribution: Skin effect is neglected (valid for DC and low-frequency AC).
- Constant resistance: Temperature coefficient of resistance is not applied; resistance is treated as constant. For copper, resistance increases ~0.393%/°C, so actual heating may be slightly higher.
- Copper defaults: Resistivity ρ = 1.72 × 10⁻⁸ Ω·m; Specific heat c = 385 J/kg·K (at 20 °C).
- PVC insulation limit: Typical maximum continuous temperature 70 °C; short-circuit limit ~160 °C (IEC 60364-5-52).
- References: IEC 60364-5-52 (Wiring systems), IEEE Std 242 (Buff Book — Protection), Neher-McGrath thermal model, AS/NZS 3008.1.
- This calculator is for estimation purposes only. Always consult applicable electrical codes and a qualified engineer for design decisions.