Ohm's Law
Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, with the constant of proportionality defined as the conductor's resistance, V = IR.
Curious
Think of voltage as water pressure, current as the rate of water flow, and resistance as how narrow or clogged a pipe is. Push harder (more pressure/voltage) and more water/current flows — but a narrower pipe (higher resistance) means less current flows for the same push. Ohm's law makes this water-pipe analogy mathematically precise: for many everyday materials, current is directly proportional to voltage, with resistance as the fixed constant linking them.
This simple, linear relationship — double the voltage, double the current, for the same resistance — is why Ohm's law is one of the very first equations taught in any introduction to electric circuits, and remains the starting point for essentially all circuit analysis.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| V | Voltage across the conductor | volt (V) |
| I | Current through the conductor | ampere (A) |
| R | Resistance | ohm (Ω) |
Worked example: A resistor of 220 Ω is connected across a 9 V battery. I = V/R = 9/220 ≈ 0.041 A = 41 mA. The power dissipated is P = IV = 0.041 × 9 ≈ 0.368 W.
Deep Dive
Ohm's law's microscopic origin lies in the Drude model of conduction (developed later, in 1900, by Paul Drude): electrons in a conductor accelerate briefly under an applied electric field before colliding with the lattice of atomic ions, losing their acquired momentum, and repeating this process continuously. This produces a steady-state average drift velocity proportional to the applied field, and hence a current proportional to voltage — a microscopic mechanical picture that explains why Ohm's law holds as well as it does for metals, and why it depends on temperature (higher temperature means more frequent lattice collisions, hence higher resistance for most metals).
Resistivity — the material-independent version: Resistance R depends on a conductor's specific shape (R = ρL/A, where ρ is the material's resistivity, L its length, and A its cross-sectional area) — resistivity ρ is the more fundamental, geometry-independent material property, analogous to how permittivity is more fundamental than a specific capacitor's capacitance.
At sufficiently low temperatures, certain materials (superconductors) undergo a phase transition to a state of exactly zero electrical resistance — a phenomenon Ohm's law, as a description of normal resistive conduction, does not capture, and one of the clearest experimental demonstrations that Ohm's law is an approximate, material-dependent description rather than a fundamental law of physics.
Concept Relationship Map
Requires: electric potential
Enables: RC circuits [PENDING FULL ENTRY — simulation available], Kirchhoff's laws [PENDING FULL ENTRY]
Commonly confused with: treating Ohm's law as universally valid rather than an approximation specific to ohmic materials
Sources
- Ohm, G.S. (1827). Die galvanische Kette, mathematisch bearbeitet. T.H. Riemann.
- Griffiths, D.J. (2017). Introduction to Electrodynamics, 4th ed. Cambridge University Press, Ch. 7.