Ohm's Law (solve for current)✓ verified
Electrical / Basic · Current from voltage and resistance (I = V / R)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| voltage | V | V | 12.0 | Voltage |
| resistance | R | ohm | 4.0 | Resistance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| current | I | A | Current |
The science & history
Understanding the Parameters
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Voltage $V$ — the potential difference (work per unit charge, J/C) that drives charge through the element; see Watt's Law for the deeper meaning of potential.
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Resistance $R$ — the element's opposition to current, in ohms ($1\ \Omega = 1\ \text{V/A}$). For a uniform conductor it is set by geometry and material, $R = \rho L / A$ (resistivity $\rho$, length $L$, cross‑section $A$). Larger $R$ means less current for the same voltage.
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Current $I$ — the resulting rate of charge flow (A = C/s).
Derivation and Physical Basis
Ohm's Law is not derived from more primitive definitions the way $P=VI$ is; it is a material property. Microscopically it follows from the Drude picture: an applied field $E$ gives carriers a steady average drift velocity proportional to $E$ (acceleration balanced by scattering), so the current density is
$$\mathbf{J} = \sigma \mathbf{E},$$
with conductivity $\sigma = 1/\rho$ a material constant when temperature and material are fixed. Integrating over a uniform conductor ($V = EL$, $I = JA$) gives
$$V = \frac{L}{\sigma A}\,I = I R, \qquad R = \frac{\rho L}{A},$$
and rearranging yields the calculator's form:
$$I = \frac{V}{R}.$$
Why it's a "law" only for some materials. The linear proportionality $J \propto E$ requires $\sigma$ to be field‑independent. Metals satisfy this over a wide range; semiconductors, gas discharges, and junctions do not, so their $I$–$V$ curves are non‑linear and Ohm's Law does not apply.
History
Georg Simon Ohm published the relation in 1827 in Die galvanische Kette, mathematisch bearbeitet, building on careful experiments with wires of different lengths and cross‑sections (and an explicit analogy to Fourier's law of heat conduction). His work was initially dismissed by the German academic establishment and only later recognised as foundational; the SI unit of resistance, the ohm, was named in his honour and standardised at the 1881 International Electrical Congress.
Related Concepts: Watt's Law, Resistor Voltage Divider, Kirchhoff's Laws, Power in Electrical Circuits
Notes: Registry calculator ohms-law (human‑verified). The other rearrangements ($V=IR$, $R=V/I$)
are algebraically equivalent; this card solves for current.