# Ohms Law

The voltage drop across a resistor is proportional to the current running through it.

```     +     V     -
I
/\  R /\      --->
----  \  /  \  ----
\/    \/
```

Ohm's law states that when the resistance of a device is independent of the voltage applied across it, and therefore of the current through it as well. This is often confused with the definition of resistance:

```  V = IR
```

where V is potential difference, I is the current and R is the electrical resistance. However, this equation holds at all times, even when Ohm's law does not. Ohm's law simply says that the relationship between V and I is a linear one. A material which obeys Ohm's law is known as ohmic.

The funny thing about Ohm's law is that it is not an actual mathematically derived law, but one that is supported very well by empirical evidence. There are times when Ohm's law does break down, however, because it is really an oversimplification. The primary causes of resistance to electrical flow in a metal include imperfections, impurities, and the fact that electrons bounce off the atoms themselves. When the temperature of the metal increases, that third factor increases, so that when a substance is heating up because of the electricity flowing through it, like the filament in a light bulb, the resistance actually increases. The resistance of a device is given by:

```      L     L
R = - ρ = - ρ0(α(T-T0) + 1)
A     A
```

where ρ is the resistivity, L is the length of the conductor, A is its cross-sectional area, T0 is a reference temperature (usually room temperature, 273 K), and ρ0 and α are constants specific to the material of the conductor.

Graphing V vs I with constant R, Ohm's law dictates that a straight line with a slope R will show up. Since R can change at extreme values of V and I, however, the graph will almost always be non-linear on large enough scales. Fortunately, the conditions where Ohm's Law holds are very common. A component which follows Ohm's law is called an ideal resistor.