Is there a mathematical definition for resistance because I cannot find any. On the internet I find definitions such as:
The electrical resistance of an object is a measure of its opposition to the flow of electric current. wiki
Electrical resistance is defined as the opposition to current flow in a circuit electrical4u
However these are too vague for me. They omit how to calculate it. Ohm's law fails too because it only works for Ohmic resistors.
Is there a mathematical definition for resistance ?
Here is an experimental definition of resistance. We can measure the current $I$ that flows through any object or device when we create a range of potential differences $V$ across it (other environmental factors, such as temperature, should be kept constant). We can then plot a graph of potential difference $V$ against current $I$. The resistance $R$ of the object or device at any point on this graph is defined as the slope of the graph at that point:
$\displaystyle R = \frac {dV}{dI}$
This is sometimes called the differential resistance of the device, to distinguish it from the ratio $\frac V I$, which is called the chordal resistance.
In an Ohmic resistor the graph of $V$ against $I$ will be a straight line passing through the origin, so its differential resistance and its chordal resistance will be constant and equal to one another. However, in a non-Ohmic resistor the graph of $V$ against $I$ will be non-linear. In this case, if the term resistance is used without qualification, it will usually mean differential resistance.
