Ohm's Law

欧姆定律 V = I · R

Symbol: V = I · R
Unit: V in volts (V) · I in amperes (A) · R in ohms (Ω)
Section: Power Conversion
Published: 2026-08-17
Author: By The Circuit Desk

Ohm's law states that the current through a linear resistor is directly proportional to the voltage across it and inversely proportional to its resistance, provided the temperature and the physical dimensions of the element stay constant.

The linear relation between voltage, current and resistance in a resistive element.

One loop: source, resistor, and the current it sets.

Governing relation V = I · R I = V / R R = V / I V in volts (V) · I in amperes (A) · R in ohms (Ω)

What the law actually constrains

Ohm's law is a statement about a material, not about a circuit topology. It says that the ratio V/I for a given piece of material is a constant over the range of interest. Metals at room temperature satisfy this to within a fraction of a percent; semiconductors, electrolytes and hot filaments do not. Every practical resistor datasheet therefore quotes a temperature coefficient and a maximum working voltage, because both push the element away from the linear region.

Reading it three ways

The same relation rearranged answers three different engineering questions. Which form you reach for depends on which quantity is fixed by the rest of the design.

V = I · R — find the drop across a known resistor carrying a known current (sizing, level shifting).
I = V / R — find the current a known source drives into a load (thermal and fuse checks).
R = V / I — infer an unknown resistance from a measured voltage and current (sensor front ends).

Where it breaks down

The table below lists elements that are routinely mistaken for ohmic. In each case the instantaneous ratio V/I is still defined, but it changes with operating point, so a single number cannot describe the part.

Element	V–I behaviour	Linear?
Metal-film resistor, 25 °C	Constant ratio to ±0.1 % over the rated range	Yes
Incandescent filament	Resistance rises roughly 8–12× from cold to white heat	No
Silicon PN junction	Exponential above about 0.6 V (per University of Mississippi)	No
Electrolytic solution	Polarisation, heating and gas evolution shift the ratio	No

Worked figure

A 9 V supply feeds a 470 Ω resistor. I = 9 / 470 = 19.1 mA and the dissipation is I²R = 172 mW, so a 0.25 W axial part runs at 69 % of rating — acceptable but warm. Drop the same resistor onto 5 V and the current falls to 10.6 mA with only 53 mW dissipated. Doubling the resistance to 940 Ω at 9 V halves the current again to 9.6 mA. Notice that the current tracks the supply linearly, which is exactly what makes this useful for setting bias points.

Adjacent entries

Resistance 电阻
Electric Power 电功率
Kirchhoff's Circuit Laws 基尔霍夫定律

Off the shelf

Sources

NDT Resource Center https://www.nde-ed.org/Physics/Electricity/ohmslaw.xhtml
Physics LibreTexts https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)
NIST https://www.nist.gov/pml/owm/si-units-electric-current