Robotics · Electronics basics · Grade 7

LED and resistor: Ohm’s law

Why does an LED with no resistor flash and die? Which resistor is needed?

The situation

You want to make a rear light for your bicycle: you have a red LED and two AA batteries. Your friend connected the LED straight to the battery — it flashed brightly for a moment, died and never lit again. Why does an LED need a resistor? Which resistor should you choose so that the light is bright but does not burn out? Build the circuit on a breadboard, swap the resistor, measure the current — and burn out one LED on purpose.

Topic

LED and resistor: Ohm’s law. A bicycle rear light: an LED with no resistor flashes and dies — which resistor is needed

Key ideas

Ohm's law
LED voltage
Current limit

Formulas

I = \frac{U - U_{L E D}}{R}

The current in the circuit: the LED voltage is subtracted from the source voltage, and what is left falls across the resistor (Ohm’s law).

R = \frac{U - U_{L E D}}{I}

The resistor you need: it is calculated for the current you want (usually 10–20 mA), then the nearest standard value is taken.

U = U_{L E D} + I \cdot R

The sum of the voltages: the source voltage is shared between the LED and the resistor.

P_{R} = I^{2} R = \frac{{(U - U_{L E D})}^{2}}{R}

The power dissipated in the resistor must not exceed 0.25 W for an ordinary resistor.

Theory

The circuit: source, conductor, load

Current flows only in a closed circuit: from the battery’s positive terminal through the wires and the resistor to the LED, and from it to the negative terminal. Take out the switch wire and the circuit opens — the current is zero. On a breadboard the five holes in one column are joined inside by a metal strip, so if the legs of parts land in one column, they are connected.

An LED is a light-emitting diode

An LED is not an ordinary bulb: it is a diode, which passes current in one direction only (the long leg is the anode, towards “+”). For current to flow it needs a certain voltage — $U_{L E D}$ : red ≈ 1.9 V, yellow ≈ 2 V, green ≈ 2.2 V, blue and white ≈ 3.1–3.2 V. This voltage depends on the semiconductor material. Beyond this voltage the LED’s own resistance is very small — the current is limited not by the LED but by the resistor.

Ohm’s law and the resistor calculation

The rest of the source voltage falls across the resistor: $U_{R} = U - U_{L E D}$ , and by Ohm’s law $I = U_{R} / R$ . For example, a 4.5 V source, a red LED (1.9 V), 150 Ω: $I = (4.5 - 1.9) / 150 \approx 0.017$ A = 17 mA — exactly right. With no resistor, instead of $R$ there are only the wires and the battery’s internal resistance (a few tenths of an ohm) — the current reaches amperes.

Why an LED burns out

For an ordinary 5 mm LED the usual current is 20 mA and the absolute limit is 30 mA. Above that the die heats up: 2 times the current — in a few seconds, 50 times — instantly. The crack and the puff of smoke are signs that the die has burnt; such an LED never lights again. The resistor heats up too: $P = I^{2} R$ ; above 0.25 W it changes colour and smells.

Reverse connection and too little voltage

If you connect the LED the wrong way round (anode on the “−” side), the diode is blocked — no current flows and the LED does not light, but it withstands a reverse voltage of up to 5 V (it is not damaged). It does not light either when the source voltage is below $U_{L E D}$ : a blue LED (3.1 V) with two AA cells (3 V) barely flickers or does not light at all — whatever resistor you fit, it does not help.

About the model

The circuit is calculated by nodal analysis. The LED model is piecewise: below $U_{L E D}$ there is no current, above it a resistance of 2 Ω (in a real LED the voltage rises slightly with current). The battery’s internal resistance is included (AA from ≈ 0.15 Ω, a PP3 ≈ 1.7 Ω). Heating is a simple thermal model: current above 30 mA accumulates over time; real LEDs differ slightly, but this is the order of magnitude.

Did you know?

The first visible (red) LED was made in 1962 by Nick Holonyak at General Electric; since then LEDs have been everywhere, from torches to phone screens.
The bright blue LED was made in 1993 by Shuji Nakamura (Nichia); for this discovery Isamu Akasaki, Hiroshi Amano and Shuji Nakamura received the Nobel Prize in Physics in 2014 — thanks to the blue LED, white LED lamps appeared.

Inside the experiment

A real board in a hand-inked isometric drawing: turn it, place the parts, wire the circuit, write and upload the code — current and voltage are computed at once, and a wrong connection burns a part. Inside are missions, theory, a quiz and a guided tour.

More experiments in this section

The electric circuit: a torch — Grades 5–6
Breadboard: rows — Grades 5–6
Resistors: the colour code — Grade 7
Voltage divider and potentiometer — Grade 7