Capacitive reactance in twin and earth

All cables have some form of capacitance, simply because the conductors act as plates, and the insulation acts as the dielectric between the plates.


The longer the cable, the more capacitance, because the plates effectively increase in size as the conductors get longer.


And that is what forms the capacitive reactance.


In a multicore cable, coiling the cable has little, if any, effect on its capacitance.



In a round 3-core (Line, Neutral and Earth) cable, with insulation on all 3 cores, there is equal capacitance between each pair of conductors.


In flat twin-and-earth cable, there is equal capacitance L-PE and N-PE, but the capacitance between L and N conductors is much less, as they are further apart, and there are two layers of insulation.

This is slightly more complex than your post. Single wires have an inherent inductance, effectively in series with the conductor. In a cable (and let's say just 2 wires at the moment) there is a capacitance between the wires perhaps 150pF/metre, but varies with the size of the conductors and distance apart. The inductance might be 20 nH/metre. If you sketch this out you will find you have low-pass filter configuration, but there is a difference, which is that because both capacitance and inductance are continuous along the length (that is there is a value for each however long one measures, say 1mm) the low pass effect is not seen and we have a "transmission line" instead. At 50Hz or so we do not see transmission line effects on short cables (100s of metres) but we do on long lines on pylons for example, because it is related to the transmission wavelength (about 60km at 50Hz).


A loop "impedance" test is concerned with the cable and Earth return path resistance plus the series inductance reactance at 50 HZ. The inductive reactance is very tiny compared to the resistance and is largely ignored except on long lengths of the largest cables (the kind which it is difficult to lift a couple of metres). It is not affected by the cable capacitance because this is a parallel effect and very tiny, and does not affect the fault current.


David CEng etc.

Thank you for explaining that made perfect sense.

If you want some numbers to conjour with, typical 2.5mm twin and earth measures between 60 and 100 picofarads from L or N to E with the unused core floating  and rather less L to N with E floating.

Capacitance is a measure of the energy stored in the electric fields around and between conductors at differing voltages - there does not have to be anything that actually  looks like plates - that is just a good  shape for max C in minimum volume. (a plump human on a step ladder has about 500 - 1000 pF to the rest of the planet, and may feel a small tingle from a live wire despite being insulated to DC.)


Inductance per unit length is a measure of the energy stored in magnetic fields around moving charges (currents) and for that typical cable again is about 1 micro henry per metre if only one core is carrying current; but if the currents in the cable are balanced so current in  L = minus current in N the round loop inductance is quite a lot less than the sum of the inductances of the two cores, as the magnetic fields oppose and overlap and partly  cancel - the figures Dave quoted are for a line pair.


As per above, all these effects are normally negligible at 50Hz unless you have very long lengths or are interested in effects that are a small fraction of  the main current and voltage.

mike.

Inductance per unit length is a measure of the energy stored in magnetic fields around moving charges (currents) and for that typical cable again is about 1 micro henry per metre if only one core is carrying current; but if the currents in the cable are balanced so current in  L = minus current in N the round loop inductance is quite a lot less than the sum of the inductances of the two cores, as the magnetic fields oppose and overlap and partly  cancel - the figures Dave quoted are for a line pair.



Thanks , didn't know that either but makes perfect sense.

It is why the reactive voltage drop in trefoil groups of cables is lower than in widely spaced singles. Again, no use at 'normal' scale, but at higher power or higher frequency it can be a trick worth pulling.

M.