Ohm's Law

Intuition

The garden-hose picture

Think of electricity in a wire like water in a garden hose. Voltage is the water pressure pushing from behind. Current is how much water actually flows. Resistance is how much the hose fights the flow — a long, thin hose resists more than a short, fat one.

Ohm's law is just the common-sense rule connecting the three: push harder and more flows; squeeze the hose and less flows. In numbers: a 9 V battery across an 18 Ω resistor pushes 0.5 A of current through it. Swap in an 18 V supply — double the push — and you get exactly double the flow: 1.0 A.

That's the whole law. Everything else on this page is the same idea, made precise and pushed to its limits. What's remarkable — and not obvious — is that for most conductors this proportionality holds exactly over a huge range: the graph of current against voltage is a dead-straight line. Materials and components that behave this way are called ohmic. Not everything is (a diode isn't, as you'll see later), which is precisely why the components that are ohmic are so useful: they're predictable.

Practitioner

Using it: the working triangle

Cover the quantity you want and read off the rest: V = I × R, I = V ⁄ R, R = V ⁄ I. Keep units strict — volts, amperes, ohms — and convert prefixes before calculating (10 kΩ is 10 000 Ω; 25 mA is 0.025 A). Most wrong answers with Ohm's law are unit slips, not maths slips.

You'll use this constantly: sizing a resistor to set a current, working out what current a circuit draws, or finding an unknown resistance from two multimeter readings.

Pair Ohm's law with the power formulas early — they answer "will this part get hot?", which matters as much as "what current flows?":

Engineer

The physics and the fine print

Ohm's law is an empirical law — a summary of how conductors behave, not a law of nature you can derive from first principles alone. Its microscopic form says the current density in a material is proportional to the electric field driving it, with the material's conductivity as the constant. Integrate that over a uniform bar of material and the familiar V = IR falls out, with R set by geometry and resistivity: long and thin means high R, short and fat means low R.

The law's real content is linearity: R is constant, independent of the applied voltage. A component is ohmic if its I–V plot through the origin is a straight line whose slope is 1/R. Resistors, wires and most metals at constant temperature qualify. Devices like diodes, filament lamps (whose resistance climbs as they heat) and anything with a threshold are non-ohmic — Ohm's law still defines an instantaneous ratio V/I at any operating point, but that ratio is no longer a constant you can carry between calculations.

Professional

Where the simple law earns its asterisks

In professional work you still use V = IR dozens of times a day — but you track when R is not the constant the schematic claims:

Temperature. Every real resistance drifts with temperature (specified as a tempco in ppm/°C — see Resistor Tolerance & Precision). Copper wiring rises about 0.4 % per °C: harnesses and motor windings have meaningfully different resistance cold versus hot, and current-sense calculations that ignore self-heating chase their own tail.

Non-ohmic reality. Semiconductor junctions, varistors, thermistors, arcs and electrolytes all have curved I–V characteristics. For small excursions around a bias point, engineers linearize: the local slope defines a dynamic resistance (lower-case r), which is Ohm's law reborn as an approximation with a stated region of validity — the pattern you'll meet again in small-signal models.

Parasitics and frequency. At AC, resistance generalizes to impedance; above a few MHz even a "pure" resistor carries inductance from its leads and capacitance across its body. The DC law is the f → 0 limit of a richer picture.

Measurement realities. At low resistances, lead and contact resistance corrupt V/I measurements — hence four-wire (Kelvin) connections on current-sense resistors. At very high resistances, meter loading does the corrupting (Meter Loading Effects).

None of this dethrones the law. It defines the boundaries inside which the one-line version is exact enough — which is most of everyday electronics.