Whether a conductor survives a fault before the protection clears it, by the standard adiabatic method. Applies equally to cable conductors and earthing conductors.
Standard method — stated scope limits apply
Fault
Use the protection's total clearing time — relay operating time plus circuit-breaker opening time, not the relay alone.
Conductor
k comes from the applicable standard for your conductor and insulation combination — it depends on the material and on the permitted initial and final temperatures, so it isn't assumed here.
Enter fault and conductor data.
About This Calculation
A cable subjected to fault current for the time it takes upstream protection to clear the fault must not exceed its short-circuit thermal withstand limit — the adiabatic (no-heat-loss-to-surroundings) approximation used for this calculation assumes all the fault energy heats the conductor directly, which is genuinely accurate for the short durations (typically under 5 seconds) real protection clearing times fall within. This check exists because a cable correctly sized for normal load current can still be thermally destroyed by a fault current it was never checked against, if protection clearing time is too slow relative to the cable's cross-sectional area.
Frequently Asked Questions
Why is the adiabatic assumption valid here when it clearly isn’t for continuous loading?
Heat conduction away from the conductor into surrounding insulation and air takes real time — measured in tens of seconds to minutes for typical cable constructions. Over the sub-5-second durations most fault-clearing times fall within, essentially none of that heat has had time to escape, so treating all the energy as staying in the conductor is a genuinely accurate, not just conservative, approximation.
What is the k-factor in the cable withstand formula and where does it come from?
k depends on the conductor material (copper vs. aluminum) and the cable’s insulation type’s maximum permitted short-circuit temperature (which is higher than its continuous operating temperature) — it is derived from the conductor’s specific heat, resistivity, and the temperature rise permitted between normal operating temperature and the insulation’s short-circuit damage limit.
Why does a slower upstream breaker require a bigger cable, all else equal?
The withstand formula shows required cross-sectional area scaling with the square root of clearing time — a breaker that takes 4 times longer to clear a fault requires a cable with twice the cross-sectional area to absorb the proportionally larger total energy (I²t) without exceeding its thermal limit.
Does this check replace normal ampacity sizing?
No — it is a separate, additional check. A cable must pass BOTH normal ampacity/voltage-drop sizing for continuous load AND short-circuit thermal withstand for fault conditions; either one alone can be the governing constraint depending on the specific installation and protection scheme.