Resistors The component that makes everything else safe to use. Three jobs — limit current, divide voltage, define a logic level — cover almost every resistor you will ever place.

1. Current limiting — in series with an LED, or a transistor base. The resistor takes the leftover voltage and turns it into a defined current.
2. Voltage division — two resistors making a lower voltage from a higher one, or converting a sensor's resistance into a readable voltage.
3. Pull-up / pull-down — holding a logic input at a defined level so it is never floating. Almost always 10kΩ; the exact value barely matters.

A resistor converts electrical energy into heat in proportion to current squared. That is its entire physics, and it is why the power rating exists.

// 4-band: digit digit multiplier tolerance
brown black red  gold  = 1  0  ×100 ±5%  = 1000Ω = 1k
red   red   brown gold = 2  2  ×10  ±5%  = 220Ω

0 blk  1 brn  2 red  3 org  4 yel  5 grn  6 blu  7 vio  8 gry  9 wht

Honestly, most people stop decoding bands and measure with a multimeter or buy a kit in labelled compartments. Do the latter, and keep it sorted from day one — loose mixed resistors are a genuine time sink and the reason many kits go unused.

// dropping a 5V signal to 3.3V for an input pin
R1 = 1.8k, R2 = 3.3k
Vout = 5 × 3300 / (1800 + 3300) = 3.24V  ✓

The two limitations that matter

• A divider is not a power supply. It only holds its output voltage when whatever you connect draws negligible current compared with the divider itself. Feeding a high-impedance input pin: fine. Powering a module: it will sag and misbehave. Use a regulator. The calculator above shows exactly how much a load pulls the output down — try entering 1000Ω.
• Current is always flowing through the divider, wasting power continuously. Very low values waste battery; very high values (above ~100kΩ) become noise-sensitive and are affected by the input they feed. For general use, keep the total in the 1kΩ–100kΩ range.

Replace one resistor with a variable one — a thermistor, LDR or potentiometer — and the output voltage tracks a physical quantity, ready for an ADC input.

Choosing the fixed resistor: pick a value near the sensor's mid-range resistance. An LDR that swings 1kΩ (bright) to 100kΩ (dark) pairs well with about 10kΩ — that places the useful range in the middle of the ADC's span rather than squashed at one end.

Pull-ups and pull-downs

Without one of these, an unconnected input pin picks up stray charge and reads randomly — which looks exactly like a flaky sensor or a software bug. Most microcontrollers have internal pull-ups you can enable in one line of code; use them and save a component.

• Discoloured, then open circuit — overloaded. It ran beyond its power rating, and the smell is memorable. Before replacing it, work out why more current flowed than you intended.
• Reads as zero ohms in circuit — you are probably measuring a parallel path through the rest of the board, not the resistor. Lift one leg or measure with power off and the component isolated.
• Value drifts when hot — normal, small, and only matters in precision timing or measurement circuits.