Ohm's Law & Electric Power — Voltage, Current, and Where the Heat Goes
The core idea
Electricity's two everyday quantities are voltage (V, volts) — the electrical "pressure" pushing charge — and current (I, amperes) — how much charge flows per second. A conductor resists that flow with resistance (R, ohms). The governing relation is Ohm's law:
V = I · R — voltage equals current times resistance.
Push twice the pressure through the same resistance and twice the current flows. Every load — heater element, motor winding, LED strip — is just a resistance with a job.
Power follows directly: P = V · I (watts), and substituting Ohm's law gives P = I² · R. The second form is the important one, because it says heat dissipated in any resistance grows with the square of the current. Double the current and the heating quadruples. This is why every conductor has two personalities: it carries energy toward a useful load, and it unavoidably converts a little of that energy into heat in its own copper — loss that the I²·R form governs.
This is also why the mains is high voltage. For the same delivered power P, current drawn is I = P/V: at 230 V, a 2.3 kW kettle pulls 10 A; at 115 V it would pull 20 A — and the same household wiring would dissipate four times the heat (I² doubled twice). Voltage is raised so current stays modest and the wires stay cool. (When currents do change, note resistance R in ohms is a property of the conductor itself; power drawn by a load is set by V·I together.)
Real-world example — household wiring and extension cords
A wall socket circuit is protected at 16 A — not because copper melts near 16 A, but because sustained current near that figure heats the cable's insulation toward its limit. Now the classic abuse: a long, thin extension reel still coiled on its drum, feeding a 2 kW heater (8.7 A). The coiled loop cannot shed heat — no airflow, neighbouring turns warming each other — and its own I²·R loss can raise the reel to the temperature where insulation softens and fire risk begins. Uncoil the drum; the heat spreads harmlessly along the whole length. Electricians and fire brigades find the same physics every winter.
Common pitfall
Beginners mix up what stays constant when computing power: they grab P = V·I but pair a nameplate voltage with a guessed current — or divide the other way. Keep the discipline: V is across the load, I is through it, and the load's own resistance or nameplate decides the pair. Second trap: forgetting that I²·R loss in a cable is on top of the load's power — a long undersized cord doesn't just waste heat, it also drops voltage, so a drill at the far end runs weaker. The wasted watts and the dimmer tool are the same phenomenon seen twice.