Ohm's law: the one relationship everything hangs on

Voltage pushes, resistance resists, and current is what results: V = I × R.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

In beta. This lesson was written for Hone and has not yet been checked by a licensed electrician. Practice material, not professional advice. What that means.

What it is for

Every fuse you size, every wire you pick and every fault you trace comes back to this line. The day a motor draws twice what it should, the first question is which of the three changed, and an electrician who cannot rearrange the law is guessing.

How to think about it

Write the law, cover the letter you do not know with a finger, and read the other two. Then put the units on before the number: amps, volts, ohms.

Worked example

V = I × R

The law. Any two give you the third.

12 V = I × 4 Ω

A 12-volt battery across a 4-ohm heater. Two knowns, one unknown.

I = 12 / 4 = 3 A

Rearranged for I, then the arithmetic. Three amps.

R = V / I: 120 V / 5 A = 24 Ω

The same law, covering R. A lamp drawing 5 A from the wall is a 24 Ω load.

Your turn

A 24 V supply across 6 Ω. Write the line that gives the current.

I = 24 /

The trap

Dividing the wrong way. 4 / 12 is 0.33 and looks like a plausible current. The units catch it: ohms over volts is not amps.

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