Physics · Electricity

Ohm's Law

Reference entry · last updated 20260909

Ohm’s law is the empirical observation that the current through many conductors is directly proportional to the voltage across them. In the form used for circuit analysis, voltage equals current times resistance, written V = IR.[1]

1. First principles and definitions

Charge is measured in coulombs (C). Current is charge flow per second, measured in amperes (A). Voltage is energy per unit charge, measured in volts (V). For any two-terminal component, the ratio of the voltage across it to the current through it is defined as its resistance R.[2]

\[R \equiv \frac{V}{I}, \qquad 1\,\Omega = 1\,\mathrm{V/A}\]

The unit of resistance is the ohm (Ω), a coherent SI derived unit equal to one volt per ampere.[2][4] Ohm’s law is the further claim that, for certain materials, this ratio stays constant as the voltage and current change, so current is directly proportional to voltage. The German physicist Georg Simon Ohm (1787–1854) first demonstrated the proportionality experimentally.[1]

Despite the name, Ohm’s law is not a law of nature like Newton’s laws or the laws of thermodynamics. It is an empirically observed phenomenon, like friction, that holds for some materials over a limited range of conditions.[1]

2. The three algebraic forms

The circuit relationship V = IR rearranges three ways, one for each quantity that might be unknown.

\[V = IR, \qquad I = \frac{V}{R}, \qquad R = \frac{V}{I}\]

Unknown	Form	Reads as
Voltage	V = IR	current times resistance
Current	I = V / R	voltage divided by resistance
Resistance	R = V / I	voltage divided by current

At fixed resistance, doubling the voltage doubles the current. At fixed voltage, doubling the resistance halves the current.[1] These forms assume R is a single fixed value. When resistance changes with temperature or with the operating point, the R used must be the value that applies at the measured conditions.[2]

3. Ohmic and non-ohmic materials

A material or component whose current stays proportional to the applied voltage is called ohmic. One that does not is non-ohmic.[1] On a current-voltage plot, an ohmic component is a straight line through the origin whose slope is \(1/R\). Many metals are close to ohmic when held at constant temperature.[1]

Non-ohmic components include diodes, whose current-voltage curve is strongly non-linear, and filament lamps, whose resistance rises as the filament heats.[1] In conducting metals, resistivity increases with temperature because stronger atomic vibrations impede electron motion. Resistance therefore depends on temperature even for an otherwise ohmic wire.[2]

\[R = R_0\,(1 + \alpha\,\Delta T)\]

Here \(R_0\) is the resistance at a reference temperature, \(\alpha\) is the temperature coefficient of the material, and \(\Delta T\) is the change in temperature.[2]

4. Power dissipation

In steady DC, the electrical power delivered to a device is the voltage across it times the current through it. For a resistor or other ohmic device, substituting Ohm’s law gives two further forms.[3]

\[P = VI = I^2 R = \frac{V^2}{R}\]

The substituted forms apply to resistors and ohmic devices, where the voltage drop is dissipated as heat. The form \(P = V^2/R\) shows that, across a fixed voltage, a lower resistance draws more power. Watts measure this rate of energy transfer.[3]

5. Worked DC example

Illustrative calculation: a 6 Ω resistor is connected across a 12 V DC supply. The current is the voltage divided by the resistance, and the power follows from any of the three power forms.

\[I = \frac{12}{6} = 2\,\mathrm{A}, \qquad P = 12 \times 2 = 24\,\mathrm{W}\]

The same 24 W follows from \(I^2 R = 4 \times 6\) and from \(V^2/R = 144/6\). If the same resistor is placed across 24 V, the current doubles to 4 A and the power rises fourfold to 96 W, because power scales with the square of the voltage at fixed resistance.