Ohm's Law: the one equation everything else is built on
Three letters that explain why your phone charger gets warm.
The one relationship, three ways round
Ohm's law is a single fact written three ways depending on what you are missing.
V = I × R have current and resistance, want voltage
I = V / R have voltage and resistance, want current
R = V / I have voltage and current, want resistance
In ordinary language: voltage is the push, current is how much flows, and resistance is how hard it is to get through. Push harder and more flows. Make it harder to get through and less flows. Everything else in this subject is built on those two sentences.
💡 The units matter more than they look. V in volts, I in amperes, R in ohms. If a question gives you milliamperes, convert to amperes before substituting — a value in mA left unconverted makes your answer wrong by a factor of a thousand, and it is the single commonest arithmetic slip in this topic.
Here's something worth pausing on: why does a thin wire get hot while a thick one stays cool, carrying the same current? The answer is the single most useful relationship in electrical engineering. In 1827 Georg Ohm found that for most materials, the current through a conductor is directly proportional to the voltage across it, provided temperature stays constant. The constant of proportionality is what we call resistance.
V = I × R
V = voltage across the element (volts, V)
I = current through it (amperes, A)
R = resistance of the element (ohms, Ω)
Rearranged: I = V/R R = V/I
Ohm's law is not a universal law of nature — it's a property of certain materials. A resistor obeys it; a diode, a transistor and a filament lamp do not. That distinction is exactly what the "linear vs non-linear" question later in this section is testing.
Reading it three ways
I = V / R With V = 24 V, R = 12 Ω, I = 2 A, P = 48 W.
Hold V and double R: the current halves. Hold R and double V: it doubles. Notice power does neither — it follows V squared, which is why a small rise in voltage heats a resistor far more than you expect.
The same equation answers three different questions, and exam problems rotate between them. If you know any two quantities, the third follows.
🔍 Which form do I use?
Find IGiven a supply voltage and a known resistance — "how much current will flow?" Use I = V/R.
Find VGiven a current through a known resistor — "what voltage is dropped across it?" Use V = IR. This is the form you use constantly in KVL problems.
Find RGiven measured voltage and current — "what is this component's resistance?" Use R = V/I.
Worked numerical 1 — the basic case
A 12 V battery is connected across a 470 Ω resistor. Find the current, and the power dissipated.
I = V/R = 12 / 470 = 0.02553 A = 25.53 mA
P = V × I = 12 × 0.02553 = 0.306 W ≈ 306 mW
Check with the other power forms:
P = I²R = (0.02553)² × 470 = 0.306 W ✔
P = V²/R = 144 / 470 = 0.306 W ✔
A quarter-watt resistor would be running past its rating here — this is why component selection matters, not just the current answer.
Worked numerical 2 — the trap version
When the current through a resistor is doubled, by what factor does the power dissipated change?
P = I²R
If I becomes 2I: P' = (2I)²R = 4I²R = 4P
Power increases FOUR times, not two.
Power depends on the square of current (or voltage). Doubling current quadruples heat. This is the single most common "conceptual" mark in the paper. It also answers the question we opened with. Why does the thin wire get hot? Same current, but higher R — so more I²R heat, packed into less material.
The resistance behind the resistance
Resistance isn't arbitrary — it comes from the material and its shape:
R = ρL / A
ρ (rho) = resistivity of the material (Ω·m)
L = length of the conductor (m)
A = cross-sectional area (m²)
Longer wire → more resistance. Thicker wire → less resistance. That's the full answer to why household wiring for a heavy appliance is deliberately thick.
💡 Exam angle: expect a 2-mark direct calculation, or Ohm's law buried inside a larger network problem. Always write the formula, substitute with units, then answer — method marks are awarded even if arithmetic slips. And memorise all three power forms (VI, I²R, V²/R); which one is fastest depends on what the question gives you.
Syllabus points
V = IR; applications (numerical)
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