The LED Circuit

Your first real electronics calculation, end to end. One LED, one resistor, one battery — and every number justified.

The circuit

5V (+) ---[ 220Ω ]---+---[ LED >| ]--- GND (-)
                      (long leg)  (short leg)

Current flows: 5V → resistor → LED's long leg → LED → short leg → GND. One loop, as promised in chapter 1.

The calculation

The LED drops ~2V (its forward voltage — red LEDs ~2V, blue/white ~3V; the datasheet says exactly). The resistor must drop the rest:

V_resistor = 5V - 2V = 3V

Pick a safe current — 15 mA is bright and comfortable:

R = V / I = 3V / 0.015A = 200Ω

Check (verified): 200Ω. Nearest standard value: 220Ω (see Reading Resistors).

Now verify with the actual 220Ω — what current really flows?

I = 3V / 220Ω = 0.0136A = 13.6 mA

Check (verified): 13.6 mA — safely under the LED's typical 20 mA max and the Arduino pin's ~20 mA limit.

And the resistor's power:

P = V × I = 3V × 0.0136A = 0.041 W

Check (verified): 0.041 W — a standard ¼ W resistor loafs along at a sixth of its rating.

What if there's no resistor?

The LED tries to drop its 2V across ~zero resistance:

I = 3V / ~0Ω → enormous

In practice: very bright for a second, then the LED dies — sometimes taking the Arduino pin with it. This is the single most common beginner hardware death, and it's a 5-cent part away from never happening.

Varying the design

Supply	LED drop	Target current	R = (Vs−Vf)/I	Use
5V	2V	15 mA	200Ω	220Ω
3.3V	2V	10 mA	130Ω	150Ω
9V	2V	15 mA	467Ω	470Ω
5V	3V (blue)	15 mA	133Ω	150Ω

Check (verified): (5−2)/0.015 = 200; (3.3−2)/0.01 = 130; (9−2)/0.015 = 466.7; (5−3)/0.015 = 133.3. Same formula every time — R = (supply − LED drop) / current. Memorize that line; it's the most-used equation in hobby electronics.

Next: Soldering