Ohm's Law — V = IR

Ohm's law V = IR explained: voltage, current and resistance, when the law holds, and a worked circuit example.

V = IR

Voltage equals current times resistance.

What it means

Ohm's law says current is pushed by voltage and opposed by resistance. Double the voltage across a fixed resistor and twice the current flows; double the resistance and the current halves. It is the reason circuits can be designed on paper before being built: pick the voltage you have and the current you want, and the required resistance falls out of the equation. Remember it describes a property of materials (ohmic behavior), not a law of nature — a light-bulb filament's resistance climbs as it heats, and the simple proportionality bends.

Variables

Symbol	Name	Unit	Meaning
$V$	Voltage	V	Electric potential difference across the component
$I$	Current	A	Rate of charge flow through the component
$R$	Resistance	Ω	Opposition to current flow

Assumptions

Conductor is ohmic — resistance does not change with current or temperature
Steady (DC) conditions
Uniform temperature throughout the conductor

Derivation

Ohm's law is an empirical observation, not a universal law: for many conductors at constant temperature, measured current is directly proportional to applied voltage. The constant of proportionality is 1/R. Materials that violate it (diodes, filaments) are called non-ohmic.

Worked example

Problem

A current of 2 A flows through a 6 Ω resistor. What voltage appears across it?

Given:

I = 2 A
R = 6 Ω

Write Ohm's law: $V = IR$
Substitute: $V = 2 \times 6$
Multiply: $V = 12\ \mathrm{V}$

12 V across the resistor

Pushing 2 amps through 6 ohms of resistance requires a 12-volt drop — the resistor converts that electrical energy into heat. This is the calculation behind choosing resistor values in every simple circuit.