a good explanation of the speed of electricity in cables from Archis Gore a professor
...I already had someone correct me about electron speed in cabling when I mentioned it in the 'speaker cabling being equal length for all channels'- apparently, it's not the same as the speed of light.
Part 1
Summary from article = The Speed of Electricity
every electron in the wire must move 0.37455 cm each second according to Archis Gore's explanation following and the speed of light is 299,792,458 m per second exact.
So based on Archis Gore's analysis below elecricity flow at 1.2493 e-11times the speed of light.
Especially read the end explanation I high lighted in red
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The Speed of Electricity
I have always noticed how many of our students are ignorant on the very basis of what science is. There are people who know a lot about a lot but are totally ignorant on very basic issues. The educational system is partly a reason for this and the lack of student’s curiosity is the other.
Currently trends are towards increasing creativity amongst students. But what we lack is curiosity. Before creativity, there must be curiosity. There must be a motivation to know something just for the sake of it.
The concept of the speed of electricity is a very common example that I use to confuse many of my peers. And many people are surprised of how totally distant their guesses are from my estimates. During this article, we shall try to calculate the speed of electricity ourselves to get a general idea of the order of magnitude.
I am going to ask you to do something that I always ask all the people to whom I explain this concept. Please try to make an estimate of the speed of electricity after you have read the specifications of the system described below. This estimate must be made orally and just an order of magnitude would be fine. Many answers that I generally get to this question is the speed of light. Some even go on to comment that since they have learned that the speed of light is the absolute limit to how fast anything can travel, they are stopping short of naming a higher value.
I must comment that the speed of electricity is a very subjective issue based on the current, conduction and resistance of the circuit. So I am considering the following well defined system.
Let us consider a common light bulb working on DC (direct current, this will simplify calculations). Let us assume the household voltage of 250 volts, and a standard copper wire of radius 1mm connecting the bulb serially to the voltage source. Assume also, that the bulb consumes 40 watts of power. This rating is decided by the manufacturing company considering the resistance of the bulb and the voltage that is going to be applied to it. This eliminates the need for us to know the resistance of the bulb. Let us assume for the sake of convenience that the copper wire has zero resistance (this will in fact give us a higher estimate for the speed of our electrons).
Now let us first clearly define the speed of electricity that we mean. We shall try to estimate the average distance covered by an electron in the wire in one second when the entire circuit is closed.
First lets calculate the total current that will flow through the bulb. Since we have a voltage of 250 volts and a wattage of 40 watts, the current should be equal to power/voltage=40/250=0.16A.
Now lets divert to another angle. Let us consider a 1cm long segment of the wire used in our circuit. We shall try to estimate the total charge that that segment of wire holds at any instant. We can find the volume of the segment as follows:
Volume=P * r2 * l
Where r is the radius of the wire and l is the length of the segment.
Hence, the volume comes out to be (in cubic metres):
Volume=3.14 * (0.001)2 * (0.01) = 3.14 * 10-6 * 10-2 = 3.14 * 10-8 cubic metres
Now we consider the average number of atoms of copper that this segment of wire must be holding. The density of copper is 8.96 kilograms per cubic metre and its atomic weight is 63.546. Atomic number of copper is 29 which we will require later on in our calculations.
Hence our segment of wire weighs approximately:
Mass=3.14 * 10-8 * 8.96 kilograms = 2.81344 * 10-7 kilograms = 2.81344 * 10-4 grams
Generally 1 atomic mass unit = 1.6603 * 10-24 grams. Since the atomic weight of copper is 63.546, the weight of one atom of copper in grams is given by:
Weight of 1 atom of copper = (1.6603 * 10-24 * 63.546 ) grams = 105.5054238 * 10-24 g
= 1.055054238 * 10-25 kg
Now, we must find out how many atoms of copper are crammer up into 2.81344 * 10-7 kg of copper. We simply divide the total weight of the copper segment by the weight of an individual atom of copper as follows:
Number of copper atoms in segment=2.81344*10-7/1.055054238*10-25 = 2.66663 * 1018
Just to be sure, we shall calculate the same using a different approach. Avogadro’s number gives us the number of molecules (in case of copper, the number of atoms) of a specific substance contained in one gram-mole (molecular weight in grams) of that substance. Hence, one gram mole of copper should contain 6.0221367 * 1023 atoms. The molecular weight of copper being 63.546, one gram-mole of copper is 63.546 grams. Now using some middle school algebra, knowing that 63.546 grams of copper contains 6.0221367 * 1023 atoms, we can easily calculate the number of atoms in 2.81344 * 10-7 kilograms (equivalent to 2.81344 * 10-4 grams) of copper. The calculations are shown below:
63.546 grams : 6.0221367 * 1023 atoms
2.81344 * 10-4 grams : ? atoms
x=6.0221367 * 1023 * 2.81344 * 10-4 / 63.546 = 0.2666245 * 1019 atoms
= 2.666245 * 1018 atoms
This matches our estimate and hence we are probably on the right track. We shall now find the average between the two values and consider that average as the number of atoms of copper contained in our segment of wire of radius 1mm and length 1cm. Hence,
Average number of copper atoms in segment are = 2.6664375 * 1018
One atom of copper contains 29 electrons since its atomic number is twenty-nine. Now we know that not all electrons in an atom are free to move while conducting current. This is the part on which I am unsure and am making a safe assumption. The electron configuration of copper is 2-8-18-1. I will assume that only one electron per atom is allowed to move since only one electron is present in the valence band (outer most band). This is actually a more complicated matter involving primary and secondary quantum numbers and sub-orbitals of equal energy and so on but we shall do away with all this. If in fact more electrons are allowed to move in an atom, then our calculations will give a higher value than the actual value. So our value will be a very safe estimate.
Now since the charge on each electron is 1.6021892 * 10-19 coulomb, an atom of copper will carry movable charge equivalent to:
Movable charge on copper atom=1.6021892 * 10-19 coulomb
The charge on the segment of wire under consideration is:
Charge on segment = number of atoms in segment * charge on each atom
= 2.6664375 * 1018 * 1.6021892 * 10-19 C
= 4.272137364975 * 10-1 C