Ohm's Law Explained
Ohm's law is the simple, powerful rule that ties together the three quantities at the heart of every electric circuit: voltage, current, and resistance. It says that the current I flowing through a component is proportional to the voltage V across it, with the resistance R as the constant of proportionality:
V = I R
The relationship was established by the German physicist Georg Simon Ohm, who published it in 1827 after painstaking experiments measuring how current flowed through wires of different lengths and thicknesses. His work was so undervalued at the time that he resigned his teaching post; today the SI unit of resistance, the ohm (Ω), carries his name.
What each quantity means
It helps to think of charge flowing through a wire like water flowing through a pipe. Voltage (volts, V) is the electrical "pressure" that pushes charge along — the energy delivered per unit charge. Current (amperes, A) is the rate of charge flow, how much passes a point each second. Resistance (ohms, Ω) is how strongly the component opposes that flow, the way a narrow pipe restricts water. Rearranging V = IR gives the two forms you use most in practice: I = V/R (more voltage or less resistance means more current) and R = V/I (resistance is the ratio of the two).
Is it really a "law"?
Ohm's law is best understood as an empirical relationship that holds for a large class of materials — called ohmic conductors — rather than a fundamental law of nature like conservation of energy. For a metal wire at fixed temperature, R is genuinely constant, so a graph of current against voltage is a straight line through the origin. That straight-line behaviour is Ohm's law. Many components, however, are non-ohmic: their resistance changes with voltage, current, or temperature, so the V–I graph curves. The relation R = V/I still defines a resistance at any operating point for these devices, but it is no longer a single fixed number.
A common misconception
Ohm's law is not universal. A diode, a filament lamp, and a transistor all violate the straight-line rule — a diode barely conducts below a threshold voltage and then conducts heavily, while a lamp's resistance rises sharply as its filament heats. So "everything obeys Ohm's law" is false; the correct statement is that ohmic materials do, over a wide but finite range, and recognising where the law breaks down is as important as knowing where it holds.
Related references
Resistivity and Resistance
The resistance of a conductor depends on its material and geometry: R = ρL/A, where ρ is the resistivity (Ω·m), L is the length, and A is the cross-sectional area. Resistivity is a material property: copper ≈ 1.7×10⁻⁸ Ω·m; nichrome (heating wire) ≈ 1.1×10⁻⁶ Ω·m; silicon ≈ 10³ Ω·m.
Resistivity increases with temperature for metals (more lattice vibrations scatter electrons): ρ(T) = ρ₀[1 + α(T − T₀)], where α is the temperature coefficient. For semiconductors and thermistors, resistivity decreases with temperature, enabling temperature sensing applications.
Kirchhoff's Laws and Circuit Analysis
Ohm's law alone describes individual resistors; Kirchhoff's laws handle complete circuits. Kirchhoff's Voltage Law (KVL): the sum of voltages around any closed loop is zero. Kirchhoff's Current Law (KCL): the sum of currents at any node is zero (charge conservation). Together with Ohm's law, these three relationships allow the analysis of any resistive circuit.
For resistors in series: R_total = R₁ + R₂ + ... (voltages add, current is the same). For resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + ... (currents add, voltage is the same).
Power Dissipation
The power dissipated as heat in a resistor is P = IV = I²R = V²/R. Joule heating is the basis of electric heaters, incandescent bulbs, fuses, and toasters. In power transmission lines, low current (achieved with high voltage via transformers) minimises I²R losses — this is why the national grid operates at hundreds of kilovolts.
Worked Examples
Example 1: A 12 Ω resistor is connected to a 6 V supply. Find the current and power.
I = V/R = 6/12 = 0.5 A. P = IV = 0.5 × 6 = 3 W.
Example 2: Two resistors 4 Ω and 6 Ω are in parallel across 12 V. Find the total resistance and total current.
1/R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12. R = 12/5 = 2.4 Ω. I = V/R = 12/2.4 = 5 A.
Non-Ohmic Devices and Real-World Limitations
Ohm's law (V = IR with constant R) holds for many materials at fixed temperature but fails for others. A diode allows current in only one direction; its I-V curve is exponential, not linear. A transistor has current controlled by a gate voltage, enabling switching and amplification. Incandescent bulbs violate Ohm's law because their resistance rises with temperature — resistance at operating temperature (~2,700 K) is about 10× higher than at room temperature.
In practice, Ohm's law provides an excellent first approximation for metallic conductors at constant temperature. The microscopic basis is the Drude model: conduction electrons scatter off lattice ions with a mean collision time τ, giving resistivity ρ = m/(ne²τ), where n is the electron density. This derivation reveals why higher temperature (shorter τ due to more vigorous lattice vibrations) increases resistivity in metals.
Key Equations Summary
Ohm's Law: V = IR. Resistance from geometry: R = ρL/A. Series: R_total = R₁ + R₂ + ... Parallel: 1/R_total = 1/R₁ + 1/R₂ + ... Power dissipated: P = IV = I²R = V²/R. KVL: sum of voltages around any closed loop = 0. KCL: sum of currents at any node = 0. The SI unit of resistance, the ohm (Ω), is named after Georg Simon Ohm, who published his law in 1827 after systematic experimental study of current flow through wires. Modern understanding derives resistance from electron-phonon scattering as described by the Drude and Sommerfeld models of metallic conduction.
Ohm's Law underpins the design of every electronic circuit. From simple resistor voltage dividers used in sensor circuits, to the internal resistance of batteries (which reduces terminal voltage under load), to the skin-effect resistance of conductors at high frequencies — all are analysed using V = IR. Kirchhoff's laws extend this to arbitrary circuit topologies, forming the foundation of circuit analysis taught in every electrical engineering curriculum worldwide.
References and further reading
- Griffiths, D. J. Introduction to Electrodynamics, 4th ed. Cambridge University Press, 2017.
- Jackson, J. D. Classical Electrodynamics, 3rd ed. Wiley, 1998.