Ohm's Law
The linear relation between voltage, current, and resistance — V = IR — that is fundamental to circuit analysis.
Ohm's law states that the current I through a conductor is directly proportional to the voltage V across it, with the proportionality constant called resistance R: V = IR. It was formulated by Georg Simon Ohm in 1827 and is the first quantitative relation most students meet in electrical engineering. The law defines the ohm (Ω) as volts per ampere, and it underlies the entire analysis of resistive circuits.
Ohm's law is a property of a class of materials and devices, not a universal law of nature. Resistors, wires, and most heating elements obey it over wide ranges (ohmic devices); semiconductors, diodes, and transistors do not — their current grows exponentially or nonlinearly with voltage (non-ohmic devices). Even ohmic materials deviate at extreme voltages or temperatures, when the resistance itself changes. Circuit analysis therefore starts by checking the V–I characteristic of each component.
Combinations of resistors follow directly from the law. In series, the same current flows through each resistor and the voltages add, so R_total = R₁ + R₂ + …; in parallel, the same voltage appears across each and the currents add, so 1/R_total = 1/R₁ + 1/R₂ + …. These rules are the basis for voltage dividers, current dividers, and impedance matching, and they combine with Kirchhoff's circuit laws to solve arbitrarily complex networks.
The law also links power: since P = VI and V = IR, power dissipated as heat is P = I²R = V²/R. This is why high-voltage transmission lines are efficient — for a given delivered power, raising the voltage lowers the current, and losses drop as I²R, which is one reason three-phase electric power is transmitted at hundreds of kilovolts. Ohm's law remains the foundation of everything from LED resistor sizing and battery calculations to the design of power distribution systems.
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circuits electricity resistance voltage
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