Electric Current and Ohm's Law

Introduction

Recall from our last unit that when a charged particle is placed in an electric field the charge experiences a force. However, electric fields do not exist inside conductors when the charges are static. If you create a potential difference between two parts of the conductor you can start the charges moving. Once they're in motion we see an electric field inside the conductor that keeps the charges moving. Just like changing the strength of the field determines the force and subsequent motion of individual charges, changing the potential difference (which well now always refer to as voltage) affects how the charges move. In our analysis, the voltage will be provided by batteries.

Let's review concepts you learned in a previous physics course. Previously you learned that current, I can be defined by how much charge moves through a conductor in a given amount of time. Given a continuous conducting path between the terminals of a battery, current will flow.

Note: Remember that electrons are the charges in motion when an electric current is present. However, for historical reasons, we analyze the current flow as if it were positive charges in motion, moving from the positive towards the negative terminals in a battery. This is referred to as conventional current.

For ohmic conductors, the strength of the current is directly proportional to the voltage provided and inversely proportional to the resistance of the conductor. This information is codified in Ohms Law: V=IR. Where V is voltage (measured in volts, V), I is current (measured in amperes or amps for short, A), and R is resistance (measured in ohms, Ω).

In electric devices, the current can be controlled by varying the voltage (think dimmer switches) or by having a fixed voltage and introducing resistors. Resistors are physical devices that have set levels of resistance to the flow of electric charges. Like water flowing over a dam, as charge moves through a resistor it is moving from a higher potential to a lower potential. This means that, though the current stays the same, the charges experience a voltage drop. Using Ohms Law you can calculate the voltage drop across any given resistor.

To get a quick review of Ohms Law and how it applies to electric circuits (coming up in the next lesson), watch this presentation. It may take a few moments to load.

Resistivity

Resistivity

The resistance of a material is determined by its physical properties. Many resistors are made from wound spools of wire. It has been experimentally determined that the resistance of a wire is directly proportional to its length L and inversely proportional to its cross-sectional area A.

In this resistance equation, ρ is known as the resistivity of the conductor. This is an intrinsic property with units of ohm-meters (Ω•m).

Note: Do not confuse the symbol for resistivity for density. Contextual clues should make it obvious that the same symbol is used for a different purpose in this unit.

Combining the resistivity equation with Ohm's Law you should notice that objects with a lower resistivity will allow more current to pass through them when connected to a voltage source. Silver and copper have two of the lowest resistivities among metals, with silver coming out slightly lower than copper. Why don't we then use silver wiring? There are several factors, but one of the biggest has to be cost.

You should also notice that larger cross-sectional area wires will also conduct more current for a given voltage source. If you go to the store to buy an orange extension cord you'll notice the biggest difference between them, besides length, is something called gauge. The gauge is a reference for the cross-sectional area of the wire. In a less-than-intuitive situation, the smaller the gauge number, the larger the cross-sectional area. So, if you were going to be running a longer extension cord for a high-energy use device, you would prefer a 10-gauge cord over a 16-gauge cord.

Resistivity Practice

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