Ohm's Law Explained, With the Resistor Math

Four quantities, three letters, and one relationship that explains most of what happens in a DC circuit. Here is Ohm's law with the two examples engineers actually reach for: sizing an LED resistor, and checking whether a component will survive.

ElectricalBy Jul 9, 20265 min read
Ohm's Law Explained, With the Resistor Math — ListCalc

The relationship

Voltage (V, volts) is the push. Current (I, amps) is the flow. Resistance (R, ohms) is the restriction.

V I R
Cover the value you want — the remaining two show the formula
To findFormulaUnits
VoltageV = I × Rvolts
CurrentI = V ÷ Ramps
ResistanceR = V ÷ Iohms
PowerP = V × I = I² × R = V² ÷ Rwatts
Unit discipline saves you every time: use volts, amps and ohms — not milliamps. 20 mA is 0.02 A. Mixing prefixes is the source of most wrong answers by a factor of 1,000.

Example 1: sizing an LED resistor

A red LED with a 2 V forward voltage, running at 20 mA, from a 9 V supply. The resistor must absorb the voltage the LED does not:

V across resistor = 9 − 2 = 7 V
R = 7 ÷ 0.02 = 350 Ω

350 Ω is not a standard value. Choosing the next value up — 390 Ω — gives 7 ÷ 390 = 17.9 mA, slightly dimmer and safely inside the LED's rating. Rounding down instead would overdrive it.

Now check the resistor survives

P = I² × R = 0.0179² × 390 = 0.126 W. A standard quarter-watt (0.25 W) resistor handles that with margin to spare.

Enter any two values — the rest solve live.Ohm's law calculator →

Example 2: what a load draws

A 12 V heating element drawing 5 A:

That 60 W figure is what sizes the fuse, the wire and the power supply. A supply rated 12 V at 4 A will not run it.

Why components burn out

Almost always because power dissipation was never calculated. Power rises with the square of current, so doubling the current quadruples the heat:

Power in a 47 Ω resistor
50 mA0.12 W
100 mA0.47 W
200 mA1.88 W
A quarter-watt part fails somewhere in the middle row
Rule of thumb: pick a power rating at least twice the calculated dissipation. Resistors derate as they heat, and a part running at its exact rating runs hot enough to damage what is around it.

Where Ohm's law stops being enough

The law holds for resistive DC circuits. Two common places it needs extending:

Sizing a DC system such as solar or 12 V wiring? The same power relationship — watts, amps and volts — is what turns panel ratings into real output.

Run your own numbers

Ohm's law Voltage drop Solar panel

FAQ

What is Ohm's law?
Voltage equals current times resistance: V = I × R. Rearranged, I = V ÷ R and R = V ÷ I. Know any two of the three and the third follows.
How do I calculate the resistor for an LED?
Subtract the LED's forward voltage from the supply voltage, then divide by the desired current. A 2 V LED at 20 mA on a 9 V supply needs (9 − 2) ÷ 0.02 = 350 Ω. Use the next standard value up — 390 Ω — which is safer for the LED.
What is the power formula in a circuit?
P = V × I. Combined with Ohm's law it also gives P = I² × R and P = V² ÷ R. Use whichever form matches the two values you already know.
Why does my resistor get hot or burn out?
Because it is dissipating more power than its rating. A resistor passing 0.2 A with 47 Ω dissipates I² × R = 1.88 W — which destroys a quarter-watt part. Calculate the dissipation and choose a rating at least double it.
Does Ohm's law work for AC circuits?
For purely resistive AC loads, yes, using RMS values. Once capacitance or inductance is involved, resistance is replaced by impedance and phase angle matters, so the simple form no longer tells the whole story.

Sources

Primary references used for the figures and rules on this page.

  1. SI Units — NIST
  2. Fundamental Physical Constants — NIST