Ohm's Law Calculator

While V = IR is a convenient macroscopic relation, Ohm's law is not a fundamental law of nature, but an empirical approximation. Microscopically, it is expressed as the vector relation J = σE, where J is current density, σ is conductivity, and E is the electric field. In anisotropic materials, conductivity σ becomes a second-rank tensor, meaning an applied electric field can push current in a different direction. Under the classical Drude model, this linearity arises because the electric force on charge carriers is balanced by scattering against lattice vibrations (phonons) and impurities. However, this approximation breaks down under extreme conditions: in high electric fields, carrier drift velocity saturates; in superconductors, Cooper pairs undergo macroscopic quantum coherence to bypass scattering entirely (R = 0); and at the nanoscale, transport becomes ballistic, where conductance is quantized in integer steps of 2e²/h (Landauer formula), rendering the traditional concept of localized resistance obsolete.

Think of a circuit like water in a pipe: voltage is the pressure pushing charge, current is how much flows, and resistance is how much the pipe restricts it. Ohm's law V = IR ties them together, so knowing any two values gives you the third. The practical takeaway: at a fixed voltage, doubling the resistance halves the current.

Georg Ohm built his 1827 relation by direct analogy to Fourier's law of heat conduction, swapping temperature for voltage and heat flow for electric current. The same linear form reappears across physics — Fourier's heat law, Fick's law of diffusion, and Darcy's law for groundwater all share it. German academics first dismissed Ohm's work as fanciful, and he resigned his teaching post before finally winning recognition.

Water analogy: imagine the circuit as a closed pipe loop. The battery is a pump that builds up 9 V of pressure. The resistor (10 O) is a narrow section of pipe - the higher the resistance, the tighter the constriction. That pressure, fighting through that restriction, forces a steady flow of water: 0.9 A (900 mA) of current. Double the pressure - double the flow. Double the pipe width - double the flow. That linearity is Ohm's Law.