## Resistance to the flow of electron current

Only very special substances, called superconductors (they're actually special substances placed in special situations, namely extreme cold) offer no resistance to the flow of electric current. All other substances resist the flow current to some degree.

Because of the way that electrons are arranged around their nuclei, metals tend to be excellent conductors. Some, like copper (Cu), silver (Ag) and gold (Au) are better than others, like lead (Pb), but all resist the flow of electric charge (current) to some degree.

Electrical resistance of a material is a property of that material, and its size and temperature. It is a result, like most of physics and all of chemistry, of the way electrons behave when bound to atoms.

If you know a bit about chemistry, the conducting properties of metals arises from how their electrons in d-orbitals arrange and behave in bulk materials.

## Unit of resistance: The Ohm

The unit we use to measure and compare electrical resistance in materials and in electrical and electronic circuits is the Ohm, defined on the right → .

Resistance can range from a few pico-Ohms () in good conductors to many Giga-Ohms () in insulators.

The base units of Ohms (1 Ω = 1 Kg·m2s-3A2) seem a bit complicated, but you generally won't need them except in special situations. For now, just know the rough range of resistance for conductors and insulators. We'll use Ohms a lot to do circuit calculations.

By the way, Ohms is capitalized because it's a person's name: Georg Simon Ohm.

## Resistivity in materials

The resistance of materials depends on their size (more about that below), so when we compare resistance to the flow of electricity, we need to put everything on the same scale – in other words, we need to make size not matter. The unit used in the table on the left is Ohms per meter (Ω/m) and it's called resistivity.

You can see that the things you would expect to conduct electricity have low resistivity, and the things you hope don't, insulators like glass and rubber, have very high resistivities.

Notice that the difference in resistivity between a good conductor and a good insulator can be many orders of magnitude of resistivity.

Also notice that many materials commonly held to be good conductors, like water, are actually not so good.

Silicon (and other semi-metallic elements around it in the periodic table) can either conduct or resist current in different circumstances, and they are called semiconductors – and there's a whole industry built around them!

Conductors have low resistance to the flow of electric current, while insulators have high resistance. Some materials in the middle, like silicon and germanium can act, in the right circumstances, as either a conductor or an insulator. These are called semiconductors.

## Resistance is proportional to size

The resistance of a material is a property of the identity (atomic & molecular structure) of the material and its size and shape. You can think of resistance to the flow of electric current much like resistance to the flow of water in a pipe:

If the pipe is narrow, the amount of water you will be able to push through will be limited.

If the pipe is long, the small amount of attraction of the water for the walls will add up and slow it down.

In a wire like the one shown below, the resistance is proportional to the length, and inversely proportional to the cross-sectional area. The longer the wire the greater the resistance, and thicker wires have less resistance. Mathematically, the resistance proportionality statement is:

The constant of proportionality is ρ (the Greek letter "rho"), the resistivity of the material. Resistivity is an intensive property, and length and area are extensive.

The

## Choke points

Let's say you have a long and very conductive wire through which you're running an electric current. The wire is a good conductor so the resistance is low, and we would say that the resistance of the whole system (we'll call it a circuit later) is low.

Now interrupt that wire with a small element that has a high resistance – it could just be a thin piece of wire like the fine wires in an incandescent light bulb – and the resistance of the whole system will just be the resistance of that least conductive piece. It's a choke point for the flow of current.

You can think of electricity like water flowing through pipe. You can get a lot of water to flow through a 10 cm diameter pipe, but if there's just one small section that has a diameter of 1 cm, then that section will determine the overall flow. It's the rate-limiting or current-limiting element of the system.

Later we'll use this idea to create different currents around the same loop of current in circuits.

### Incandescent light bulbs are resistive devices.

Incandescent light bulbs operate using the choke-point principle above.

Current is directed through a very fine wire (the horizontal section in the center of the bulb on the right) that is resistive because of the choice of material, and because it is very thin.

Because of the high resistance and high current, electrons moving in the wire experience a "friction" that heats the wire. In fact, it's heated so hot that it emits visible light.

You may have seen that metal objects heated in a fire glow red. It's the same principle here except that the wire gets much hotter. The hotter the wire, the more light is emitted in the visible and ultraviolet range.

Source: Wikipedia Commons

## Resistance can be temperature-dependent

Very often, and to varying degrees, the electrical resistance of a material can depend on the temperature of the material.

When a material, such as a wire, is relatively cold, its atoms move more slowly and don't oscillate as far from their equilibrium positions in the metal. The path of a charged particle, like an electron, through the wire might look like this:

But if the substance is hotter, its atoms will oscillate more rapidly, and will travel farther from their equilibrium positions, and thus the probability of a collision with the traveling charge will be greater:

The path of such a charge will be more convoluted, so it will take longer, on average, to travel the same distance in cold material

This charge dependence of resistance can be important in many kinds of electric circuits, so it's worth keeping in mind.

## Ohm's law and the flow of current

What we're really interested in is regulating the flow of electric current to do useful things. We'd like to make the flow of current predictable and to be able to manipulate it.

It turns out the the flow of current through a material is directly proportional to the driving force, which we've called potential (or more commonly "voltage") in another section, and it's inversely proportional to the resistance of the material. That's known as Ohm's law, and it's written like this:

Ohm's law is one of the most important relationships in all of the field of electricity and magnetism. If we want more current, we can either

• increase the potential (voltage) or
• decrease the resistance.

Later you will see electric circuits in which the potential, current and resistance are fixed, and those in which each can depend upon other things, such as frequency of switching current on and off. All of this leads to all of the wonderful electronic devices to which we've become so accustomed.

Ohm's law is usually written on one line as a product, V = IR.

Ohm's law: Potential is current multiplied by resistance.

V   =   IR

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