Ohm's law is a relationship between voltage, current and resistance for an electrical component or material that behaves ohmically under specified conditions. It is commonly written as V = I R, where V is the potential difference across the component, I is the current through it and R is its resistance. The law states that, when resistance remains constant, current is directly proportional to voltage.
Doubling the voltage across a constant resistance therefore doubles the current, while halving the voltage halves the current. Rearranging the relationship gives I = V divided by R and R = V divided by I. Ohm's law is one of the foundational relationships in elementary circuit analysis, but it is important to recognise that not every electrical device obeys it over its entire operating range. It describes a specific type of electrical behaviour rather than being a universal law that every material and component must follow under every condition.
The historical basis of Ohm's law is associated with Georg Simon Ohm, a German physicist who investigated the relationship between electrical quantities during the nineteenth century. Ohm published his major work on the mathematical description of conduction in 1827. The modern formulation uses voltage, current and resistance, although the underlying experimental observations concern how electrical current responds to potential differences in conducting systems. The SI unit of resistance, the ohm, is named after him.
Ohm's work contributed to the development of quantitative electrical science by establishing a mathematical relationship that could be tested experimentally and applied to circuit analysis. Modern electrical engineering uses Ohm's law together with Kirchhoff's laws and component models to analyse networks ranging from simple resistors to complex electronic systems.
A material or component is described as ohmic when its current voltage relationship is linear over the relevant operating conditions and the resistance remains approximately constant. A graph of voltage against current for an ohmic resistor is a straight line passing through the origin when there are no additional offsets or relevant nonlinear effects. The slope of a voltage versus current graph represents resistance.
If current is plotted against voltage instead, the slope represents conductance, which is the reciprocal of resistance. Real resistors are approximately ohmic over their specified operating range, but their resistance can change with temperature, applied voltage, frequency and other conditions. Consequently, whether a device is called ohmic depends on the range and conditions being considered. A component can behave approximately ohmically in one region and nonlinearly in another.
Many important electrical components are non ohmic. A semiconductor diode has a strongly nonlinear current voltage relationship, allowing current to increase dramatically once its forward voltage region is reached under suitable conditions. An incandescent lamp filament becomes hotter as current increases, and its resistance rises substantially with temperature, so its current voltage characteristic is not a straight line. Thermistors deliberately exploit strong temperature dependence, while varistors have resistance that changes substantially with applied voltage.
Transistors and other semiconductor devices have operating characteristics governed by more complex physical relationships. Even when Ohm's law does not describe a complete device, local or differential resistance can sometimes be defined from the slope of its current voltage characteristic. Therefore, saying that a component does not obey Ohm's law does not mean that voltage, current and resistance are unrelated; it means that a single constant resistance cannot adequately describe the component over the relevant operating range.
Ohm's law is particularly useful because it allows circuit quantities to be calculated from known values. If a 100 ohm resistor has 10 volts across it, the current is 0.1 amperes under ideal ohmic conditions. The same relationship can be used to calculate voltage drops across resistors in series, currents through branches and equivalent circuit behaviour. In a series circuit, the same current flows through ideal series components, so the voltage drop across each resistor is determined by its resistance.
In parallel circuits, components share the same voltage while their currents depend on their individual resistances. Ohm's law can therefore be combined with series and parallel resistance rules to analyse larger networks. For more complicated circuits, Kirchhoff's current and voltage laws extend the analysis beyond simple one component relationships.
Ohm's law is closely connected with electrical power. Substituting V = I R into P = V I gives P = I squared R, while substituting I = V divided by R gives P = V squared divided by R. These equations allow the power dissipated by an ohmic resistor to be calculated when different combinations of voltage, current and resistance are known. This is important when selecting resistor power ratings and estimating heat production.
A resistor may have a correct resistance value but fail if excessive electrical power causes its temperature to rise beyond its safe operating limit. The relationship also helps explain why a low resistance path can draw a very large current when connected across a substantial voltage, which is one of the central electrical mechanisms involved in short circuits.
Ohm's law has limitations that are important in real electrical engineering. Resistance can vary with temperature, mechanical strain, magnetic effects, light exposure, frequency, electric field strength and material state. Some systems contain capacitors and inductors whose behaviour depends on time and frequency rather than simply a constant resistance. In AC analysis, impedance generalises resistance to include frequency dependent effects associated with inductance and capacitance.
Ohm's law can still be expressed in complex form as V = I Z when impedance is used in the appropriate sinusoidal steady state framework. In semiconductor physics, microscopic transport may also become nonlinear under strong fields or other conditions. Therefore, Ohm's law is best understood as a highly useful constitutive relationship for ohmic behaviour rather than as a complete theory of all electrical phenomena.
The practical importance of Ohm's law comes from its simplicity and broad usefulness in electrical measurements, troubleshooting, education and engineering design. Multimeters use measurements of voltage and current to calculate resistance, although the instrument applies its own test conditions and the result may not represent a constant resistance for nonlinear components. Engineers use Ohm's law when selecting current limiting resistors, estimating voltage drops, designing sensor circuits and checking whether measured circuit values are consistent with expected operation.
It also provides a basic framework for interpreting electrical faults. An unexpectedly low resistance can produce excessive current, while an unexpectedly high resistance can cause reduced current or an increased voltage drop across a faulty connection. Understanding when Ohm's law applies, when it is only an approximation and when a more advanced model is required is more important than simply memorising the equation.
