How can Ohm law be used to calculate the electrical resistance of a piece of wire?

Answer 1

Ohm's law establishes the relationship between the current flowing in a conductor (represented by I), the potential difference across the two ends of the conductor (represented by P), and the resistance offered by the conductor (represented by R) through which current is flowing. Thus, general Ohm's law calculations based on only Ohm's law involve finding one of the three quantities.

Answer

While you can always use the ratio of voltage to current to determine the resistance of the wire, there is no guarantee that the wire is obeying Ohm's Law!

This is because Ohm's Law only applies when the ratio of voltage to current is constant for variations in voltage. For example, Ohm's Law doesn't apply to tungsten wire, because its resistance changes markedly for variations in voltage.

There is a general misunderstanding of Ohm's Law that it applies to all materials. This is not true, as it only applies to 'linear' or 'ohmic' materials.

Answer 2

Indirectly.

Ohm's Law states that 'the current in a wire at constant temperature is directly proportional to the potential difference across that wire'. No mention of 'resistance', so far!

Another way of expressing Ohm's Law is that for Ohm's Law to apply, the ratio of voltage to current must remain constant for variations in voltage. Well, when Ohm reached this conclusion he did so after testing a variety of conductors, and realised that the 'constant' of this ratio changed from conductor to conductor, and realised that whatever that constant was (1) a property of a particular conductor, and (2) it represented an 'opposition' to the fflow of current. He named this opposition 'resistance'.

So the answer to your question is that you do not get a definition of resistance from Ohm's Law, only a realisation that resistance exists, and that can be determined from the ratio of voltage to current.