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If a constant current has to be driven through a resistor it needs a certain voltage or potential difference across the outlets of the resistor.
If the voltage is changed it is plausible to expect a corresponding change of the current. What is not evident is the question if this relation is linear, if the current changes proportional to the voltage.
Under normal conditions a proportional relation is rather seldom. If the current changes, normally the temperature of the resistor and therefore its resistance changes. This implies a non-linear relation between voltage and current. If, however, the temperature of the resistor and all other properties (length, cross section) remain constant, it has been experimentally proven that for metallic and for most solid state conductors there exists a strict proportional relation between voltage and current.
Conclusion: If a constant current I is driven by a voltage V through a resistor with resistance R and if all external parameters remain constant we have: V/I = constant. This relation was first detected by the physicist Ohm and is called Ohm´s law.
By convention this constant, which is characteristic for the specific resistor, is used as definition for the resistance R.
R = V/I. The unit of resistance is Ohm, abbreviated as Ω, in honour of the German physicist Georg Simon Ohm (1789-1854).