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# Length of cable

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#### Jako13!

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Does the length of cable de rate the cable as it creates a greater resistance and as a result heats up the cable reducing its current carrying capacities?

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#### Spoon

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Does the length of cable de rate the cable as it creates a greater resistance and as a result heats up the cable reducing its current carrying capacities?

No.
What is does affect is the voltage. That's why you calculate the volt drop of circuits.
If the volt drop is too high then the cable size will have to increase.

#### Simon47

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No. Think about it - if you keep the current the same but double the length, then you double the resistance and double the heat generated. But, you have also doubled the length of the cable - so the amount of heat generated per length of cable is exactly the same.

#### pc1966

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Not directly, as already said the heat loss per unit length is the same.

But when it comes to coping with the overload under fault conditions the situation is rather different. The let-through fault "energy" (the I2t term) for an OCPD generally increases at small overloads because the 't' term increases much faster than the 'I^2' term decreases.

So for fault conditions a long cable can end up suffering more thermal stress because it took a lot longer for the OCPD to disconnect. For a fuse the curve is fairly simple, dropping down and flattening off as you get to the worst-case PFC actually having the least I2t term!

But a MCB is a lot more complex, and it depend on which region you are in (thermal trip, or "instantaneous" magnetic trip). Here is an example from the Hager commercial catalogue:

You can see that when you hit the magnetic trip region at {3-5 * In} then the fault energy drops massively as the disconnect time drops from 5-25 seconds to tens milliseconds or so.

However, unlike a fuse the MCB does not disconnect that much faster as PFC increases to allow a shorter 't' to offset the greater 'I^2' aspect. So once you get beyond a couple of kA fault currents then a similar rating BS88 fuse lets through less energy.

#### DefyG

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Strange way of wording it Jako but in simple terms yes. I think this is what you are getting at!
If you have for example a 3% VD with 20A at 50m and extend the cable, that 3% volt drop can only be achieved by de-rating the circuit current (effectively de-rating ccc of the cable for a particular circuit). As the circuit current would be less than before, I'm not sure of the significance of any heat generated!

#### pc1966

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I think we are all looking at the OP's statement from differing points of view!

Typically there are several different limits on a cable that have to be taken in to account when designing the circuit:
1. The thermal limit of CCC. This is a product of both the cable thickness (hence I2R loss per unit length heating it) and the environment it is in (thermally insulated, in duct, open air, etc) that alters how easily the heat escapes, but in itself is independent of the length. (post #3)
2. Voltage drop limit. Here a long cable may end up much heavier than the CCC limit simply to avoid too much VD (posts #2 & #5).
3. Fault disconnection time limit. This is depends on both the OCPD characteristics and the Zs value (i.e. PFC) which depends on the cable resistance (R1 + R2) and that is length-dependant. So (much like VD) can result in additional conductor size being needed to meet safe disconnection times.
4. The fault let-through energy (post #4) depends on the disconnection time and so has a thermal aspect for survival - the adiabatic calculation to see what a fault would do the insulation as an infrequent stress which might require a shorter disconnect time than the shock-protection limits in the wiring regs.
So while a cable's thermal CCC is independent of length (just the current and thermal environment), the VD and fault disconnection/adiabatic limits are length-dependent factors to consider.

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#### Jako13!

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My question was if the circuit say was run in 1.5 cable and can take 10 amps if I had a long run would that reduce that 10amps sorry for being unclear. Thanks for your help guys

#### pc1966

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My question was if the circuit say was run in 1.5 cable and can take 10 amps if I had a long run would that reduce that 10amps sorry for being unclear. Thanks for your help guys
Yes, at a point you would find it fails to meet the VD or disconnection limits.

So as the length increases from near-zero you have a constant limit, the thermal CCC, but then you reach one or more points when you need to derate it to maintain either the required VD (say 5% or 3% for lights), or to allow adequate fault clearance.

#### DefyG

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I think we are all looking at the OP's statement from differing points of view!
Agreed pc1966, the wording of the question does'nt help and of course many other things to take into consideration but got the impression trainee asking a simple question looking for a simple answer! We all know though nothing is that simple or straightforward when it comes to circuit design.

#### Jako13!

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Yes, at a point you would find it fails to meet the VD or disconnection limits.

So as the length increases from near-zero you have a constant limit, the thermal CCC, but then you reach one or more points when you need to derate it to maintain either the required VD (say 5% or 3% for lights), or to allow adequate fault clearance.

So say for an example it could take 10 amps at 10 meters if we went up to 100meters would we expect that to drop to day 5 amps for example?

#### pc1966

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Probably in the majority of cases the VD limit will also deal with the disconnection time indirectly. For example, if you need 10A and have a 10A MCB or similar then at 5% VD your fault current is (up to) 20x the MCB rating, so a long cable that has its size increased to maintain VD is keeping the PFC up and clearing time down.

Where that gets in to difficulties is when you have a higher resistance CPC (e.g. T&E with 2.5 L/N and 1.5 E, or SWA with a steel CPC that is a much poorer conductor) or on high current circuits when your cable's R1+R2 is getting down to the supply's Ze value.

#### DefyG

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So say for an example it could take 10 amps at 10 meters if we went up to 100meters would we expect that to drop to day 5 amps for example?
Maybe, you would need to limit the circuit current but you really need to do some proper circuit calcs to be sure. It wont drop automatically to 5A as in your example.

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