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Index of Subjects The following is bit too detailed, perhaps, but ... ... the undersea cable problem was investigated conceptually I think first by Lord Kelvin in the late 1800s. This is casually known to later physiologists, because of the close parallel to nerve conduction along 'passive' nerve axons (ones without nerve impulses). In both cases there is a certain significant capacitance per unit length, in the cable because (as Chris says) there is a significantly thick insulation with a finite dielectric constant, necessary to prevent current from leaking out of the conducting core into the surrounding sea water (at roughly ground potential). In the nerve fiber, the membrane around the nerve cell (or any animal cell) comprises a molecular bilayer about 5-7 nanometers thick, made largely of phospholipids. The dielectric constant of these lipids is relatively constant, similar to olive oil, so all animal cell membranes have a specific capacitance close to 1 µF/cm^2, pretty much a biological constant (one microfarad per a one centimeter square of membrane surface). If a DC current step is applied between one end of the nerve/cable and the fluid outside, the voltage inside changes quasi-exponentially to the voltage of the source. As it proceeds along the cable, the voltage gets smaller because of leakage through the 'resistance' of the membrane, as ions move through actual molecular protein channels embedded in it. It also gets slower, because the initial current has to discharge even more capacitance as distance increases. The current flows both through the leakage resistance R and the capacitance C (according to the product of the two, R*C), charging the cable or membrane depending on whether -V or +V is applied. The result is that a signal (say +V) put in at one end of the cable declines inexorably to background noise level over a certain definable distance, so the cable or nerve would no longer be useful beyond that. So capacitance is a bad thing because it both reduces and slows down signals being transmitted, and smears them out. The solution is similar in both cases, to put a series of repeater amplifiers into the cables at determined distances, to periodically boost the signals. These boosters are the nodes of Ranvier in vertebrate myelinated nerve fibers, or a continuous 'doping' of active channels into the unmyelinated giant nerve axons of Loligo pealii mentioned recently. Invertebrates missed out on 'discovering' myelination. In squid axons, a large fraction of the current flowing down the inside of the axon is used to discharge the already-charged-up membrane capacitance, so the influence of capacitance in slowing signal transmission is a very important factor limiting impulse conduction velocity. A complementary 'clever trick' vertebrate axons use is to have up to ~100 accessory myelin membranes wind around the axon, which does two things. It increases the leakage resistance by a factor of ~100, but less widely appreciated, it decreases the capacitance per unit length by the same factor. Much less charge is then needed to discharge the lowered capacitance by the advancing impulse, so a boosted impulse can 'jump' from node 1 to node 2 etc much more quickly than otherwise. As a result, vertebrate axons only 10 microns in diameter use much less ATP energy to conduct ~6 times faster that squid axons even 500 microns in diameter, cutting central costs more that even Harper dreamed about. I'm less sure about the limitations of a copper cable suspended in air at least several inches from the nearest ground reference (present close to the insulators, on the metal pylons). In this case, the capacitors must be large air gaps with consequently very little capacitance. At a very low frequency of 50-60 hertz in AC transmission, I imagine that capacitative losses are relatively small, but this could be wrong. Most losses presumably would come because even a copper cable has a very significant resistance to current owing to the large distances it covers, plus the inevitable losses caused by the current heating the cable. In any case, as Dave Webster says, the capacitance must be very small, so charging it to a certain voltage won't recover much charge if the cable is then allowed to discharge. Steve (Hfx) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Quoting David & Alison Webster <dwebster@glinx.com>: > Hi Chris, Steve & All, Aug 30, 2012 > Yes the capacitance of the cable would store electricity but > (and here I venture onto thin ice) the magnitude of this storage > would be vanishingly small. [agreed] > > From here onward the ice is even thinner-- > As a first approximation, when the DC source is removed then the > voltage between the two ends of the cable would not decrease to zero > immediately but would fall asymptotically as charge is drained from > the coaxial sheath. [you'd normally charge the inside at one end relative to the nearby juice outside, not between the two ends] > > The charge delivered to the destination/sec, before removal of > the DC source, would be roughly 3 x 10^10 times as great as the > charge delivered by discharge of the cable. [when the cable is charged at one end as above, the time course is not exactly exponential because the capacitance is distributed along the cable, and is governed by a more complicated 'bent' function (an error function, concocted from a series of exp functions). The discharge process is the complementary function.] > Yt, DW, Kentville ################################ > ----- Original Message ----- > From: Christopher Majka > To: naturens@chebucto.ns.ca > Sent: Thursday, August 30, 2012 10:14 AM > Subject: Re: [NatureNS] wind power storage > Hi Steve, > "Long undersea / underground high voltage cables have a high > electrical capacitance compared with overhead transmission lines, > since the live conductors within the cable are surrounded by a > relatively thin layer of insulation (the dielectric), and a metal > sheath. The geometry is that of a long co-axial capacitor. The total > capacitance increases with the length of the cable. This capacitance > appears in parallel with the load." > > Does this indicate that the capacitance of cable itself can store > electricity or am I completely off-base? ;~>
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