Ohm's law: relationship between voltage, current and resistance

Formula, units and practical interpretation

Ohm's law provides a simple way to calculate one quantity when the other two are known. If you know the voltage across a component and its resistance, the current is found by I = V / R. If current and resistance are known, the voltage is V = I R. Resistance is a property that quantifies how strongly a component opposes the flow of electric charge; it can be expressed as R = V / I. In circuit diagrams the law is applied to elements such as resistors and to whole networks under the assumption that each element behaves linearly. The SI units are important to keep straight: 1 ampere = 1 coulomb per second, 1 volt = 1 joule per coulomb, and 1 ohm = 1 volt per ampere.

Physical basis and limitations

Ohm's law is empirical: it was established by observation and experiment and holds exactly only for materials and components that show a linear current–voltage relationship, called ohmic materials. Many metallic conductors approximate this behavior over a wide range of conditions. However, some devices are non‑ohmic: their resistance changes with voltage, current, or temperature. Examples include semiconductor diodes, transistors, vacuum tubes, gas discharge lamps and incandescent lamp filaments. In such cases a single number R cannot describe the device; instead the V–I characteristic is nonlinear and must be represented by a curve or a differential resistance dV/dI. Temperature also affects resistance for most materials, so the law's simple form is valid only when physical conditions are essentially constant.

History and naming

The law is named after German physicist Georg Simon Ohm, who published experimental results and an analysis of electrical circuits in the early 19th century. His work showed that for many conductors the current varied in proportion to the applied potential difference, leading to the relation that now bears his name. The unit of electrical resistance, the ohm, was later named to honor him. Over time Ohm's law became a foundational tool for analyzing and designing electrical circuits.

Uses, examples and problem solving

Ohm's law is a staple in circuit analysis, electronics education and practical design. It is used to determine currents, voltages, and resistor values when building or troubleshooting circuits. Typical applications include calculating the current through a resistor connected to a battery, determining the voltage drop across series components, and sizing resistors for LEDs. A few common uses:

• Designing simple voltage dividers and bias networks.
• Estimating power dissipation via P = V I = I^2 R = V^2 / R (power formulas derived alongside Ohm's law).
• Checking whether a component will be overloaded by comparing expected current with ratings.

Distinctions and notable facts

Ohm's law should not be confused with the broader laws of electromagnetism: it is a constitutive relation that describes how some materials respond to an electric field, not a universal conservation law. In many modern contexts, the electric behavior of materials is treated by field equations and material models that generalize or replace a simple scalar resistance (for example, using conductivity, tensorial resistivity, or nonlinear device models). For introductory circuits and a large range of practical problems, however, Ohm's law remains the simplest and most useful relation. For further reading on circuit basics and units see electrical circuit theory and sources on current measurement, resistive components such as a resistor, and explanations of voltage and resistance.