Resistance at an operating point is R=IV, in ohms Ω. An ohmic conductor at constant temperature has current proportional to potential difference, so its voltage–current graph is a straight line through the origin. With voltage on the vertical axis and current on the horizontal axis, the gradient equals resistance. Swapping the axes changes the gradient to conductance, R1.
For a uniform wire of fixed material and temperature, resistance increases with length and decreases with cross-sectional area. Heating a metal usually raises its resistance. A filament lamp therefore need not have a constant V/I as its temperature changes. Calculate each operating-point resistance separately rather than applying one constant-resistance model to every component.
Example 1
A resistor has 6.0V across it and current 0.30A. Find resistance.
R=IV=0.306.0=20Ω.
Example 2
A wire has resistance 8.0Ω. Double its length without changing material, area or temperature. Find the new resistance.
R is proportional to length for these fixed conditions. Doubling length doubles resistance to 16Ω.
Watch out:Ohmic components do under fixed physical conditions; non-ohmic components can have changing IV.
Resistance and Ohm’s law practice | Year 11 Physics | Ascent Arcade