# Resistance and Ohm's Law

We will cover resistance, Ohms's law, resistivity, the effect of temperature, and superconductors.

If we apply a voltage across a given conductor, the current through the conductor is proportional to the voltage. If the voltage doubles, the current doubles. This holds true, or at least close to true, most of the time. We won't worry about that right now though, what we want to discuss is resistance.

We will define resistance as the ratio of the applied voltage to the current the conductor carries.

where R is in ohms, denoted by the greek letter omega, V is voltage, and I is current.
The unit ohms is named after Georg Simon Ohm (1789-1854)

Also named for Georg Ohm, is Ohm's law:

Where V is voltage, I is current, and R is resistance. This law holds for all ohmic materials. Materials which do not obey this law are known as nonohmic. An example of a nonohmic material would be a diode, which has different resistances depending on which way the current is flowing through it.

The resistance of an ohmic conductor is given by the following equation:

where R is resistance, p is the coefficient of resistivity, l is the length of the material, and A is the area of its cross-section. Good conductors have low resistivities, and good insulators large resistivities.

The resistivity of a material also depends upon the temperature of that material. The equation below shows how temperature modifies the resistivity coefficient:

where p is the new coefficient, p0 is the original coefficient, a is the temperature coefficient of resistivity, T is the temperature of the material, and T0 is a reference temperature, usually 20 °C

A very interesting field is developing, the field of superconductivity. Superconductors are materials that have absolutely no resistance in certain circumstances. These materials have a wide range of uses, and scientists are very interested in discovering a superconductor that is easy to handle. Unfortunately most superconductors have to be super-cold (sample temperatures) to show this property. The temperatures are often far too extreme to be useful in an application. Recent discoveries have raised the minimum temperature considerably. In the future, superconductors will undoubtedly play a vital role in many new technological developments.