Electric Currents

Introduction

Outline

• Electric Currents
  • The microscopic view
  • Resistivity
• Practice with the Concepts
• Discussion Points

Electric Currents and Resistance

Now we look at moving charges. ANY moving charge creates current, and we track current, as with all other electrical phenomena, in the direction of positive charge, despite the fact that in most cases, the charges moving are negatively-charged electrons.

We do not, in physics, go deeply into the chemical basis of a simple electrical cell. If you take chemistry, you will spend entire chapters learning how the electrolytes, or ions, of different substances move through acid solutions of different concentrations to create the flow of charges that result in a difference of electrons between two terminals and generate electrical current.

Microscopic electron flow

Here we are primarily concerned with the current itself. Any flow of charge is current, whether the particles carrying the charge are electrons, single-atom ions, or molecular ions. In most cases, we are dealing with a flow of electrons through wire — a flow of negative charge. By convention, we write the flow of charge through wire in that direction positive charge would flow, that is, in the opposite direction the electrons are actually flowing. This notation reflects the fact that when early physicists were first investigating electrical charge flow, they did not realize which charged particles were actually moving, but they had identified the charge that collected on a particular type of material as "negative". To be more specific, the original designation was set up by the American inventor, politician and writer Benjamin Franklin, so we have him to thank for the possibly confusing situation in modern circuit notation. To reduce this confusion, just remember that current i is always positive, regardless of the type of charge that is actually moving. You can then apply the notation of properly to whatever type of particle is moving, recognizing that if those charges are negative (as in the case of electrons), the motion of the negative particles will be in the opposite direction through the circuit.

Regardless of what type of material is actually carrying charge, if the material is moving through medium, it will be hampered by the medium. When free electrons flow through a wire, they bump into those electrons that are fixed in atoms, and the nucleus of the atoms in the metal lattice, and into each other. These collisions expend energy in the form of heat and slow down electrical flow. We can measure this resistance as a kind of "electrical friction". The difference in potential V, measured in volts, which draws the charged particles from one place to another (creating current I measured in amps), encounters a resistance R:

V = IR

IR we hold the potential difference V constant, as we would if we have a single source of potential difference such as a battery, the increase in resistance must result in an overall reduction in current. This makes sense and is analogous to sliding objects across a (mostly) smooth floor in a gravitational field. If we increase friction, we slow down the flow of objects crossing the floor. If we reduce the friction, we can increase the rate at which the objects can slide a the floor. Similarly, increasing or reducing resistance increases or reduces current flow through a circuit.

Resistivity

Just as different for materials can give rise to different coefficient of friction, different conducting materials can give rise to different levels of resistivity ρ. Unlike friction however, resistivity does depend on the cross-section area A through which the current flows, as well as the distance L through which the current flows.

R = ρ L/A

If we think of a wire as a tube through which electrons flow, we can see how increasing the diameter of the tube increases the cross-sectional area through which the electrons can flow. It's like having a bigger gate through which people can exit or enter a park. The bigger the gate, the greater the number of people who can get through at the same time. So increasing the cross-sectional area of a wire reduces the resistance, and makes it easier for more current to flow through the wire.

However, if the people are running through an obstacle course, they will run into more obstacles if the courses longer. Increasing the length L of a wire, and the number of bound electrons and nuclei that free electrons can run into increases the resistance of the wire to the current.

Some materials conduct electrons easily; they have low resistivity ρ and a resulting low resistance. Silver, with a resistivity of 1.59 * 10^-8 has a lower resistivity than tungsten, with a resistivity of 5.6 * 10^-8. If the cost were not a factor, you might think that it would make more sense to make wire out of silver than out of tungsten. But we also have to take into account the melting temperature of the water. Silver melts at a lower temperature than tungsten, so it takes less current to reach a resistance and a heat level that will melt silver wire, than it takes to reach a resistance and heat level that will melt tungsten. Some applications also require lighter weight or more resistance to corrosion from water, so there is no perfect single solution for all electrical applications.

Practice with the Concepts

Discussion Points

• Can a copper wire and an aluminum wire of the same length have the same resistance? If so, how?
• If a rectangular solid made of carbon has sides of lengths a, 2a, and 3a, to which faces would you connect the wires from a battery so as to obtain (a) the least resistance, (b) the greatest resistance?

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