A short circuit is over in a few hundredths of a second, and in that time a cable cannot lose heat. Every joule the fault puts into the conductor stays in the copper, and its temperature climbs until the protective device opens. Whether the insulation is still insulation afterwards is decided by three numbers: the fault current, the time the device takes, and the conductor's cross-section. IEC 60364-4-43 folds the first two into I²t and the material into a constant k, and the check is S ≥ √(I²t) ÷ k. This guide explains where every part of that comes from, which device settings turn a comfortable cable into a failing one, and how to check the result against a real breaker.
What happens in the first 100 milliseconds
The energy dissipated in a conductor of resistance R carrying a current I for a time t is I²Rt. Its resistance is ρL ÷ S, with ρ the resistivity, L the length and S the cross-section, and its heat capacity is the specific heat times the mass, c × δ × L × S. Divide the one by the other and the length cancels:
The temperature rise depends on I²t divided by the square of the size, and on nothing else about the installation. A long cable and a short one heat by the same amount per metre. Doubling the current quadruples the heating; doubling the size cuts it to a quarter. That is the whole physics, with one refinement: the resistivity of copper rises by about 0.4 % per degree, so the heating accelerates as the conductor gets hotter, and the exact integration produces a logarithm rather than a straight proportion.
The assumption that no heat leaves is the adiabatic assumption, and it is a good one for the durations that matter. Heat leaves a conductor through its insulation by conduction, with a thermal time constant of minutes for the sizes used in low-voltage installations; over a tenth of a second the loss is negligible, over a second it is small, and IEC 60364-4-43 applies the equation up to 5 s. The conductor is allowed to reach a stated final temperature once: 160 °C for PVC, 250 °C for XLPE or EPR. These are not working temperatures. PVC at 160 °C is soft and will deform where the cable is pressed against a tray edge, a gland or a cleat; the cable is not expected to be as new afterwards, only to still be a cable, with its insulation intact and its conductor not annealed into something else.
The equation and where k comes from
Write the resistivity as ρ20 × (β + θ) ÷ (β + 20), where β is the temperature at which the metal's resistance would extrapolate to zero (234.5 °C for copper, 228 °C for aluminium), put it into the heat balance and integrate from the initial temperature θi to the final limit θf. The result, given in Annex A of IEC 60364-5-54, is
where Qc is the volumetric heat capacity of the metal. For copper, Qc = 3.45 × 10⁻³ J/(°C·mm³) and ρ20 = 17.241 × 10⁻⁶ Ω·mm, and the square root of the constant in front is 226 A√s/mm²; for aluminium, with Qc = 2.5 × 10⁻³ and ρ20 = 28.264 × 10⁻⁶, it is 148. The logarithm carries the temperatures. PVC copper from 70 to 160 °C: ln(394.5 ÷ 304.5) = 0.259, its square root 0.509, and 226 × 0.509 = 115. XLPE from 90 to 250 °C: ln(484.5 ÷ 324.5) = 0.401, root 0.633, k = 143. Aluminium in PVC gives 76, in XLPE 94. These are the values in Table 43A of IEC 60364-4-43.
Two things follow from the logarithm. Raising the final temperature from 160 to 250 °C, a 90-degree gain, adds only 24 % to k, because the conductor's rising resistance eats part of the extra allowance. And the initial temperature matters as much as the final one: a separate protective conductor, which carries nothing before the fault and is taken to start at 30 °C, gets k = 143 for PVC copper, by coincidence the same as a line conductor in XLPE. The standard tabulates these separately in Table 54.3 of IEC 60364-5-54. Above 300 mm² the final temperature for PVC drops to 140 °C, because a thick conductor cannot expand against its insulation as freely, and k falls to 103.
The device decides: clearing time and let-through energy
The fault current at a point in an installation is what it is; the time is the protective device's, and devices differ by a factor of fifty or more.
- An MCB to IEC 60898-1 at a current above its magnetic threshold (five times its rating for a type B, ten for a type C) opens in around ten milliseconds, and because it opens while the current is still rising it never passes the full prospective current. The energy it lets through is measured, not calculated, and given on the datasheet as I²t against prospective current; the standard groups breakers into energy-limiting classes, class 3 being the tightest. For a 16 A type B in class 3 the let-through at 6 kA is limited to 35 000 A²s, against a nominal 6 000² × 0.01 = 360 000 from the clearing time alone.
- A moulded-case breaker to IEC 60947-2 on its instantaneous element clears in 20 to 50 ms and is only mildly current-limiting at 6 kA; but set it with a short-time delay so that it grades with the MCBs below, and it will sit through 0.1, 0.3 or 0.5 s of the full current before opening. Its let-through is then very nearly I² × t, and that delay is where cables fail the check.
- A fuse to IEC 60269 is strongly current-limiting at high currents, with a total I²t (pre-arcing plus arcing) on the datasheet that is small and almost independent of the prospective current once the fuse is in its current-limiting region. At lower currents the time comes off the time–current curve and can be seconds.
Because t enters the minimum size as a square root and the range of t across devices is fifty to one, the device setting moves the answer by a factor of seven, while the fault current on one board rarely varies by more than two or three. When a cable fails this check, the first question is not "how much bigger" but "why is the clearing time that long, and does it have to be". IEC 60364-4-43 also says, in 434.5.2, that for very short durations (below 0.1 s) where the asymmetry of the current is significant, and for current-limiting devices, k²S² must exceed the let-through I²t quoted by the manufacturer. That is the rule to apply for MCBs and fuses; I² × t is the rule for a breaker with a definite delay.
Where the check bites
For most circuits the current-carrying capacity or the voltage drop chooses a conductor with withstand to spare, and the check is a formality. It governs in four recognisable places.
Small tails off big transformers. A 1 000 kVA transformer at 5 % impedance delivers about 28.9 kA at its 400 V terminals; a 630 kVA unit at 4 % about 22.7 kA. A 2.5 mm² PVC copper tail feeding a control supply, a metering circuit or a panel light from the main busbar absorbs 82 700 A²s, which at 22.7 kA is used up in 0.16 ms. No breaker opens in that time; only a current-limiting fuse or MCB whose let-through at that current is below 82 700 A²s can protect it, and the datasheet has to say so. Otherwise the tail is 6 or 10 mm² for a few amperes of load, or a fuse goes at the busbar.
Long final circuits with a delayed breaker upstream. The fault current at the far end of a long circuit is lower, sometimes low enough to fall below the instantaneous pickup of the upstream device, which then clears it on its long-time element in seconds. The maximum current is at the near end and sets the near-end check; the minimum current at the far end sets the disconnection time, and the two together decide whether the device trips within the 0.4 s or 5 s that IEC 60364-4-41 allows. A far-end fault of 2 kA cleared in 5 s needs 2 000 × √5 ÷ 115 = 38.9 mm², so 50 mm²; a near-end fault of 6 kA cleared in 0.1 s needs 16.5. The far end can be the worse case.
Protective conductors. The earth path is often the afterthought: a 6 mm² protective conductor pulled alongside a 35 mm² feeder because that is what was on the van. It carries the whole fault current for the whole clearing time and is checked with exactly the same equation, with its own k. The next section covers it.
Generator-fed circuits. A standby generator delivers only about three times its rated current into a fault, decaying within a few cycles, and an MCB that would have tripped magnetically on the grid may not reach its threshold on the generator and clear thermally instead, in seconds. Low current for a long time is still I²t, and a load-shedding installation in Lahore that switches to a generator every afternoon should be checked for both sources.
Protective conductors
IEC 60364-5-54 offers two routes to the size of a protective conductor. The first is the adiabatic equation with the k values of Table 54.3 for a separate insulated conductor (starting at 30 °C: 143 for PVC copper, 176 for XLPE copper, 95 and 116 for aluminium) or Table 54.4 for a conductor that is a core of the same cable (starting at the cable's operating temperature: the line-conductor values, 115 and 143). The second is Table 54.2, a ratio to the line conductor for the same material: the same size as the line conductor up to 16 mm², 16 mm² for line conductors from 16 to 35 mm², and half the line conductor above 35 mm². The table is the simpler route and is usually more generous; the equation lets a smaller conductor be justified where the fault level and the clearing time are known.
Take the 35 mm² feeder above with a 6 kA fault cleared in 0.1 s. By Table 54.2 the protective conductor is 16 mm². By the equation, a separate PVC copper conductor needs 1 897 ÷ 143 = 13.3 mm², so 16 mm² again; a 6 mm² conductor (withstand (143 × 6)² = 736 000 A²s) would survive only 0.02 s of that fault. Two other rules apply whichever route is used: a separate protective conductor is never smaller than 2.5 mm² copper if it is mechanically protected or 4 mm² if it is not (543.1.3), and if the protective conductor is shared by several circuits it is sized for the most onerous of them. Steel conduit, trunking and cable armour used as the protective conductor have their own k values in Tables 54.5 and 54.6, and a wire armour's cross-section has to be looked up from the cable data rather than assumed.
The example in numbers
A sub-distribution board on a 400 V system, 6 kA at the board from the fault-level study, fed by 16 mm² PVC-insulated copper through an upstream moulded-case breaker whose short-time delay is set to 0.1 s to grade with the outgoing MCBs.
- I²t = 6 000² × 0.1 = 3.60 × 10⁶ A²s; √(I²t) = 1 897 A√s.
- Minimum size = 1 897 ÷ 115 = 16.5 mm². The next standard size is 25 mm²; 16 mm² is one size short, by 3.0 %.
- The 16 mm² conductor absorbs (115 × 16)² = 3.39 × 10⁶ A²s, so at 6 kA it must be cleared within (1 840 ÷ 6 000)² = 0.094 s, or for 0.1 s the current must not exceed 1 840 ÷ √0.1 = 5.82 kA. At 3.6 × 10⁶ A²s it would reach about 167 °C.
- Verdict: fails. Go to 25 mm², which absorbs 8.27 × 10⁶ A²s and would reach about 106 °C, or shorten the delay.
With an MCB at the origin instead, clearing in 0.01 s, the same 6 kA needs only 600 ÷ 115 = 5.2 mm²: 6 mm² passes. With the delay at 0.4 s it would need 33 mm², so 35. The cable short-circuit withstand calculator reproduces these figures and lets you change the device time, the material and the insulation and watch the minimum size move.
Checking it against a real breaker
The equation is the design check; the datasheet is the confirmation. Every breaker and fuse manufacturer publishes let-through curves: I²t on the vertical axis against prospective current on the horizontal, one curve per rating, sometimes one per type. Find the prospective current at the cable's origin from the fault-level study or the transformer calculator, read the I²t off the curve, and compare it with (k × S)² for the conductor: 3.39 × 10⁶ A²s for 16 mm² PVC copper, 82 700 for 2.5 mm², 29 800 for 1.5 mm². If the let-through is below the withstand, the conductor is protected at that fault level, whatever the nominal clearing time.
For a breaker with a short-time delay, use the delay setting as the time and the full prospective current, because the let-through in that region is not limited. For a fuse, use the total I²t at the prospective current, and remember that at currents below the fuse's current-limiting region the time comes off the curve and can be long. Check the far end as well as the near end, with the minimum fault current and the time the device takes at that current. And separately, check that the device's breaking capacity is above the prospective current, which is a different failure with the same cause. Ahmedonics carries out these checks on every panel and installation it designs, because the cost of a size step in copper is small next to a cable that has to be replaced after its first fault; the cable sizing guide covers the two other checks a conductor must pass.
References
- IEC 60364-4-43:2008, Low-voltage electrical installations — Part 4-43: Protection for safety — Protection against overcurrent — 434.5.2 adiabatic equation, its 5 s limit and the let-through rule for current-limiting devices; Table 43A; 434.2.1 position of short-circuit protection
- IEC 60364-5-54:2011, Low-voltage electrical installations — Part 5-54: Earthing arrangements and protective conductors — 543.1 sizing; Tables 54.2 to 54.6; Annex A derivation of k with the material constants
- IEC 60364-4-41:2005+AMD1:2017, Part 4-41: Protection against electric shock — Table 41.1 maximum disconnection times
- IEC 60949:1988, Calculation of thermally permissible short-circuit currents, taking into account non-adiabatic heating effects
- IEC 60898-1:2015, Circuit-breakers for overcurrent protection for household and similar installations — Part 1 — energy-limiting classes; Annex ZA of the EN edition for the class limits
- IEC 60947-2:2016, Low-voltage switchgear and controlgear — Part 2: Circuit-breakers — short-time withstand and delay settings of MCCBs and ACBs
- IEC 60269-1:2006+AMD2:2014, Low-voltage fuses — Part 1: General requirements — pre-arcing and operating I²t of fuse-links