Ohm's law is the first thing anybody learns and the last thing anybody thinks about. Voltage equals current times resistance. Three letters, one line.
Pair it with power equals voltage times current and you can get any of the four quantities from any two of the others. That is the whole wheel.
Nothing on that wheel is a separate fact to memorize. If you can rearrange V = I × R and P = V × I, you can rebuild every box on it from scratch.
The square is where the field lessons live
Look at P = I² × R. Power turning into heat goes up with the square of current, and straight up with resistance. That one line explains most of what burns.
Double the current through a connection and you do not double the heat — you quadruple it. A circuit running comfortably at 10 amps that creeps to 20 is dissipating four times the heat in every ohm of resistance along the way.
Which is why a loose termination is a heater
A properly made connection has very little resistance, so even at full load it makes almost no heat. Let it loosen and the contact area shrinks, the resistance climbs, and that same current is now pushed through more ohms.
To a good approximation the current does not change — the load decides that. What changes is resistance, and the power dumped into that one spot climbs with it. Heat oxidizes the metal, oxide raises resistance further, and more resistance makes more heat. And where the load is a motor or a switching power supply holding its output constant, the sagging terminal voltage makes it draw a little more current, which only tightens the loop.
It is also why a thermal scan is worth more than a visual one. A connection well on its way to failing looks exactly like a good one.
And why long runs lose voltage
A conductor is a resistor you did not want. Over a long run that resistance is enough to matter, and V = I × R says the voltage dropped across it rises with both the current drawn and the length of wire.
Which is why voltage drop is a load problem as much as a distance problem. The same 200-foot run that is fine for a lighting circuit can sag badly under a motor, because the current term went up.
- Upsizing the conductor cuts R, so it cuts the drop.
- Cutting the length cuts R the same way.
- Raising the voltage halves the current for the same power, so it halves the volts lost in the conductor — and since you are measuring that loss against twice the supply, the drop as a percentage falls to a quarter. The wasted heat falls to a quarter too, because it follows the square.
That last one is why distribution runs at high voltage and why 240 beats 120 on a long run. It is not a preference, it is the squared term.
Where the simple version stops
Everything above is direct current, or alternating current into a purely resistive load — heaters, incandescent lamps, resistance elements. Add a motor, a transformer or any switching electronics and current stops being in step with voltage, P = V × I no longer gives you the real power, and you need the power factor to finish the sum.
That is a different piece of arithmetic, and it has its own article. But it does not replace what is above; it sits on top of it.
The short version
- V = I × R and P = V × I. Everything else on the wheel is those two, rearranged.
- Heat follows the square of current. Twice the current, four times the heat.
- A loose connection raises R at one point, and the heat it makes raises R further.
- Voltage drop grows with current and with length, so it is a load problem too.
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This guide is general information to help you check your work. It is not legal advice or an official inspection, and it does not replace the requirements that apply to you, the manufacturer’s instructions, or a determination by an inspector or the authority having jurisdiction. Requirements vary by location and change over time; check the current rules where you work.
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