BS 3871 Miniature Circuit Breakers Let Through Energy

Let us work to a minimum permissible copper CSA.

cross sectional area is S in the text book, in sqmm.

S= root(I2t)/k

K~ 145 for rubbers  and 115 for PVC insulation , with certain assumptions about starting temperature.


Take our I2t value  of 90,000  (3kA and 10msec )and square root it = 300


cross section minimum is  300/115 = 2.61mmsq.

, so that implies with that breaker 2.5mm is not OK, but you are comfortably OK with all cables of 4mmsq up and larger.



I don't for one moment  think we need to use 3000 A for 0.1 seconds in this case but if you did then the 300 becomes more like 1000, and the minimum cable size is probably 10mmsq....


This does not make the installation dangerous to use, but means that if you have  short circuit fault within a short distance of the origin,  you need to inspect to see if the insulation near the CPC is damaged. Equally if the cable is damaged within a few metres of the box with the breaker in, it is not such a hard job   to replace it and as you get further out the PSSC falls due to cable resistance ( as a ready reckoner figure for cable resistance for PSSC assume 16 milliohms/metre for a single core of 1mmsq and scale for other lengths and cross sections- this under estimates, use 19 or 20 milliohms per metre for volt drops, this tends to over estimate slightly.)


(16 is a nice number for rules of thumb ,  1.6mm is nearly 1/16 of an inch and almost exactly the diameter of 16 standard wire gauge and 16 Birmingham sheet metal gauge, though not american wire, but AWG 14 is ~ 1.6mm dia. )


The saving grace is that for very thin wires the assumption that no heat leaves the copper while it is heating is not true - as the diameter shrinks, the surface area to volume ratio favours more rapid heat transfer - We know this is also true in reverse, it is why thin bacon cooks faster than thick sausages (I often make a cooked brekkie on weekends you see, so I know this sort of stuff ..)

So the idea that all in an instant the whole length of copper rises by 100 degrees and has enough stored energy to damage the surrounding insulation while doing so is something of a simplification. (and the assumption that the Adiabatic formula works from 0.1 sec to 5 sec hides some similar "let us  assume all wires are the same diameter" slight of hand)

Let us work to a minimum permissible copper CSA.

cross sectional area is S in the text book, in sqmm.

S= root(I2t)/k

K~ 145 for rubbers  and 115 for PVC insulation , with certain assumptions about starting temperature.


Take our I2t value  of 90,000  (3kA and 10msec )and square root it = 300


cross section minimum is  300/115 = 2.61mmsq.

, so that implies with that breaker 2.5mm is not OK, but you are comfortably OK with all cables of 4mmsq up and larger.



I don't for one moment  think we need to use 3000 A for 0.1 seconds in this case but if you did then the 300 becomes more like 1000, and the minimum cable size is probably 10mmsq....


This does not make the installation dangerous to use, but means that if you have  short circuit fault within a short distance of the origin,  you need to inspect to see if the insulation near the CPC is damaged. Equally if the cable is damaged within a few metres of the box with the breaker in, it is not such a hard job   to replace it and as you get further out the PSSC falls due to cable resistance ( as a ready reckoner figure for cable resistance for PSSC assume 16 milliohms/metre for a single core of 1mmsq and scale for other lengths and cross sections- this under estimates, use 19 or 20 milliohms per metre for volt drops, this tends to over estimate slightly.)


(16 is a nice number for rules of thumb ,  1.6mm is nearly 1/16 of an inch and almost exactly the diameter of 16 standard wire gauge and 16 Birmingham sheet metal gauge, though not american wire, but AWG 14 is ~ 1.6mm dia. )


The saving grace is that for very thin wires the assumption that no heat leaves the copper while it is heating is not true - as the diameter shrinks, the surface area to volume ratio favours more rapid heat transfer - We know this is also true in reverse, it is why thin bacon cooks faster than thick sausages (I often make a cooked brekkie on weekends you see, so I know this sort of stuff ..)

So the idea that all in an instant the whole length of copper rises by 100 degrees and has enough stored energy to damage the surrounding insulation while doing so is something of a simplification. (and the assumption that the Adiabatic formula works from 0.1 sec to 5 sec hides some similar "let us  assume all wires are the same diameter" slight of hand)