Ohm’s law theory

Potential difference is energy transferred per unit charge between two points. Current is charge passing a cross-section per unit time. Resistance compares the voltage across an element with the current through it. The ratio V/I can be defined at an operating point even for a nonlinear element; constant resistance over the tested range is the additional ohmic property.

For the model resistor the voltage and current are proportional while temperature and physical structure remain fixed. Raising voltage can heat a real resistor and change its resistance. A curved graph can reflect heating, a nonlinear element or measurement loading; inspect the circuit before treating it as a failure of the algebra.

A series ammeter measures the current through the resistor and should have low internal resistance. A parallel voltmeter measures the potential difference across the resistor and should have high input resistance. A real voltmeter also draws current: depending on the exact ammeter position, the ammeter can include that extra current or the voltmeter can include the ammeter voltage drop. Record the actual circuit topology.

The displayed current is in mA, but the numerical fit uses amperes. Divide a displayed mA value by 1000 before using SI equations. For example, 50.00 mA is 0.05000 A. The simulation rounds the current display to 0.01 mA. Resolution is a display increment, not an uncertainty budget or a manufacturer accuracy specification.

Put voltage V on the horizontal axis and current I in amperes on the vertical axis. Fit I = mV + b, retaining the intercept. The gradient is conductance, measured in A/V or siemens. Therefore resistance is the reciprocal of the gradient. A graph with the axes exchanged instead has resistance as its gradient; always state which graph you used.

Power dissipated in a resistor grows quadratically with voltage. At 10 V across 100 Ω the ideal current is 0.100 A and power is 1.0 W. That exceeds the continuous rating of common 0.25 W resistors; a physical apparatus needs an adequately rated component, current limiting and a suitable thermal procedure. For a fit-derived resistance, the gradient contribution is u(R) = u(m)/m². Meter calibration, voltage uncertainty, lead resistance and heating are additional effects, even if the virtual fit has zero residual.