Electrical Current

What is electric current?

Electric current is defined as the rate at which charge flows through a surface (the cross section of a wire, for example). Despite referring to many different things, the word current is often used by itself instead of the longer, more formal “electric current”. The adjective “electrical” is implied by the context of the situation being described. The phrase “current through a toaster” surely refers to the flow of electrons through the heating element and not the flow of slices of bread through the slots.

Conventional Current Direction
The particles that carry charge through wires in a circuit are mobile electrons. The electric field direction within a circuit is by definition the direction that positive test charges are pushed. Thus, these negatively charged electrons move in the direction opposite the electric field. But while electrons are the charge carriers in metal wires, the charge carriers in other circuits can be positive charges, negative charges or both. In fact, the charge carriers in semiconductors, street lamps and fluorescent lamps are simultaneously both positive and negative charges traveling in opposite directions.

Ben Franklin, who conducted extensive scientific studies in both static and current electricity, envisioned positive charges as the carriers of charge. As such, an early convention for the direction of an electric current was established to be in the direction that positive charges would move. The convention has stuck and is still used today. The direction of an electric current is by convention the direction in which a positive charge would move. Thus, the current in the external circuit is directed away from the positive terminal and toward the negative terminal of the battery. Electrons would actually move through the wires in the opposite direction. Knowing that the actual charge carriers in wires are negatively charged electrons may make this convention seem a bit odd and outdated. Nonetheless, it is the convention that is used worldwide and one that a student of physics can easily become accustomed to.

Current versus Drift Speed
Current has to do with the number of coulombs of charge that pass a point in the circuit per unit of time. Because of its definition, it is often confused with the quantity drift speed. Drift speed refers to the average distance traveled by a charge carrier per unit of time. Like the speed of any object, the drift speed of an electron moving through a wire is the distance to time ratio. The path of a typical electron through a wire could be described as a rather chaotic, zigzag path characterized by collisions with fixed atoms. Each collision results in a change in direction of the electron. Yet because of collisions with atoms in the solid network of the metal conductor, there are two steps backwards for every three steps forward. With an electric potential established across the two ends of the circuit, the electron continues to migrate forward. Progress is always made towards the positive terminal. Yet the overall effect of the countless collisions and the high between-collision speeds is that the overall drift speed of an electron in a circuit is abnormally low. A typical drift speed might be 1 meter per hour. That is slow!

One might then ask: How can there by a current on the order of 1 or 2 ampere in a circuit if the drift speed is only about 1 meter per hour? The answer is: there are many, many charge carriers moving at once throughout the whole length of the circuit. Current is the rate at which charge crosses a point on a circuit. A high current is the result of several coulombs of charge crossing over a cross section of a wire on a circuit. If the charge carriers are densely packed into the wire, then there does not have to be a high speed to have a high current. That is, the charge carriers do not have to travel a long distance in a second, there just has to be a lot of them passing through the cross section. Current does not have to do with how far charges move in a second but rather with how many charges pass through a cross section of wire on a circuit.

To illustrate how densely packed the charge carriers are, we will consider a typical wire found in household lighting circuits – a 14-gauge copper wire. In a 0.01 cm-long (very thin) cross-sectional slice of this wire, there would be as many as 3.51 x 1020 copper atoms. Each copper atom has 29 electrons; it would be unlikely that even the 11 valence electrons would be in motion as charge carriers at once. If we assume that each copper atom contributes just a single electron, then there would be as much as 56 coulombs of charge within a thin 0.01-cm length of the wire. With that much mobile charge within such a small space, a small drift speed could lead to a very large current.

To further illustrate this distinction between drift speed and current, consider this racing analogy. Suppose that there was a very large turtle race with millions and millions of turtles on a very wide race track. Turtles do not move very fast – they have a very low drift speed. Suppose that the race was rather short – say 1 meter in length – and that a large percentage of the turtles reached the finish line at the same time – 30 minutes after the start of the race. In such a case, the current would be very large – with millions of turtles passing a point in a short amount of time. In this analogy, speed has to do with how far the turtles move in a certain amount of time; and current has to do with how many turtles cross the finish line in a certain amount of time.

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