1996 Bill Beaty
How fast does electricity flow? Well, it depends on what you mean by "electricity." The word Electricity has more than one contradictory meaning, so before we can talk about its flow, we have to decide on which of several "electricities" we really mean. For a discussion of electric current, see below. But for articles about fast-flowing electromagnetic energy, see the FAQ, this energy article, or an old email.
OK, then how about this. When we turn on a flashlight, something called an "electric current" begins to happen. Inside the flashlight bulb, the thin filament-wire gets hot because there is electric current in the metal. This current is a motion of something. How fast does this "something" move? This question can be answered.
The quick answer
Inside the wires, the "something" moves very, very slowly, almost as slowly as the minute hand on a clock. Electric current is like a flow of syrup. Even maple syrup moves too fast, so that's not a good analogy. Electric charges flow as slowly as a river of warm putty. And in AC circuits, the moving charge doesn't move forward at all, instead it sits in one place and vibrates. Energy can flow fast in an electric circuit because metals are already filled with this "putty." If you push on one end of a column of putty, the far end moves almost instantly. Energy flows fast, yet an electric current is a very slow flow.
The complicated answer
Within all metals there is a substance which can move. This stuff has several different names: the Sea of Charge, or the Electron Sea, or the Electron Gas, or "charge." We often call it "electricity." Calling it "electricity" can be misleading because charge is not energy, yet many people think that electrical energy is the "electricity." It can be misleading because the Sea of Charge exists within in all metal objects, all the time, even when the metal has not been made into a wire and is not part of an electric device. If the Electron Sea is "electricity," then we must say that all metals are full of electricity. Better to call it by the name "charge-sea," and avoid the misleading word "electricity".
During an electric current, the wire stays still and the sea of charge flows along through it. When the flashlight switch is turned off and the lightbulb goes dark, the charge-sea stops moving forward. Even though it stops moving, the charge-sea is still inside of that wire. If the flashlight is again turned on and two light bulbs are connected in parallel instead of one, the electric current will have twice as large a value, and twice as much light will be created. And most important, the charge-sea of the battery's wires will flow twice as fast. In other words, THE SPEED OF THE CHARGES IS PROPORTIONAL TO THE VALUE OF ELECTRIC CURRENT; small current means low-speed charge flow, large current means high speed. Zero current means the charges have stopped. Note however that an electric current does not have just one speed. Charges speed up when they flow into a thinner wire. The high current in the lightbulb of a big flash-lantern will be much faster than the same current in the conductors in the lantern. Even though an electric current is a very slow flow of charges, we can't know the actual speed of flow unless first we know the *value* (the amperes) of the current in the wires.
If a thin wire is connected in a circuit end to end with a thick wire, it turns out that the charges in the thin wire move faster. This makes sense, it works just like water in rivers. If a huge wide river moves into a narrow channel, the water speeds up. When the channel opens out again downstream, the river slows down again. The flow in a very thin wire will be tend to be fast, even if the value of current is fairly low. This means that we can't know the speed of the flowing charge-sea unless we know how thick the wires are.
If a copper wire is connected into a series circuit with an aluminum wire of the same diameter, the charges in the copper will flow slower. This occurs because there is one movable charge per each atom in the metals, but there are more atoms packed into the copper than into the aluminum, so there is more charge in each bit of copper. When the charge-sea flows into the copper, it gets packed together and slows down. When it flows out into the aluminum, it spreads out a bit and speeds up. This means that we cannot know how fast the charges flow unless we know how dense the charge-sea is within the metal.
The speed of electric current
Since nothing visibly moves when the charge-sea flows, we cannot measure the speed of its flow by eye. Instead we do it by making some assumptions and doing a calculation. Let's say we have an electric current in normal lamp cord connected to bright light bulb. The electric current works out to be a flow of approximatly 3 inches per hour. Very slow!
Here's how I worked out that value. I know:
- Bulb power: about 100 watts, about 100V at 1A
- Value for electric current: I = 1 ampere
- Wire diameter: D = 2/10 cm, radius R=.1cm
- Mobile electrons per cc (for copper, if 1 per atom): Q = 8.5*10^+22
- Charge per electron: e = 1.6*10^-19
- The equation:
cm/sec = ________I_______ = .0023 cm/sec = 8.4 cm/hour
Q * e * R^2 * pi
This is for DC. Chris R. points out that for a particular value of frequency of AC, the "skin effect" can cause the flow of charges in the center of a wire to be reduced while the current on the surface becomes stronger. There are fewer charges flowing, and hence they must flow faster. ("Skin Effect" is stronger at high frequencies and with thick wires. The effect can USUALLY be ignored in thin wires at 60Hz power-line frequencies.)
The size of the wiggle
And about AC... how far do the electrons move as they vibrate back and forth? Well, we know that a one-amp current in 1mm wire is moving at 8.4cm per hour, so in one second it moves:
8.4cm / 3600sec = .00233 cm per second
And in 1/60 of a second it will travel back and forth by
.00233cm/sec * (1/60) = .0000389cm, or around .00002"
This simple calculation is for a square wave. For a sine wave we'd integrate the velocity to determine the width of electron travel.
So for a typical AC current in a typical lamp cord, the electrons don't actually "flow," instead they vibrate back and forth by about a hundred-thousandth of an inch.
On thinking along these lines I notice something interesting: in copper, one coulomb of movable electrons has a certain size! There are about 13,000 coulombs of free electrons per cubic centimeter of copper.
8.5*10^+22 elect/cc * 1.6*10^-19 coul./elect = 13600 Coul./cc
Therefore one coulomb would form a cube approximately 0.4mm across...
1/(13600cc^(1/3)) = 0.042 cm
HA! A coulomb in copper is about the size of a grain of sand! We can now discuss electric currents within wires as if they were cc-per-second fluid-flows inside of small hoses. If an Ampere is one coulomb per second, we're REALLY saying that an Ampere is "one saltgrain-sized blob, moving each second, squeezing itself into whatever sized wire." So, for the usual sizes of wires used in electric circuitry, if we deliver one salt-grain per second (one amp,) that's a very slow flow. The tiny saltgrains are going by: bip, bip, bip, once per second.. In 16-gauge wire the saltgrain blobs would be morphed to fill the cross-section, so they would resemble very thin stacked pancakes. In 30-gauge wire the saltgrains would be almost undistorted, and so the charges would move at about 0.4 mm/sec during a 1-amp current.
One thing's not certain in the above calculations: the charge density for copper. My above value for Q assumes that each copper atom donates a single movable electron. The email from the person below points out that this might not be true. For example, if only one in ten conduction electrons are movable, while the rest are "compensated" and frozen, then the speed of the charge flow will be ten times greater than 8.4cm/hour.
One final point. Electrons in metals do not hold still. They wiggle around constantly even when there is zero electric current. However, this movement is not really a flow, it is more like a vibration, or like a high-speed wandering movement. How should we picture this? Well, remember that we can speak of moving wind and flowing water as if they had a genuine velocity... yet a similar type of rapid wandering motion is found in the atoms of all normal liquids and gases. Even when the wind is less than one MPH, the air molecules are zooming around at hundreds of MPH. Even when there is no wind at all, the air molecules still wiggle around at the same high speeds. We usually ignore this when discussing wind, and instead take the average velocity of all molecules in a certain small volume. We call it "thermal vibration," and we see the fast movements as a separate issue. Therefore we should do the same with circuitry: the electric current is akin to wind, while the high speed wandering motions of individual electrons is akin to thermal vibrations of the air. In the above article I concentrate on the slow "electron wind" which is measured by electric current meters, and I ignore the electrons' high speed "thermal vibration."
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