Resistance, Resistors and Power
Resistivity and temperature
R = ρl/A: resistance rises with length and resistivity, and falls with cross-sectional area. Copper and aluminium are the standard conductors; nickel-chrome alloys make heating elements. Metals have a positive temperature coefficient (resistance rises with heat); carbon and most semiconductors have a negative one. A thermistor exploits this: NTC resistance falls sharply as it warms, while a PTC device can self-regulate as a heater or protection element. An LDR falls in resistance with light.
Resistors
The colour code runs black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9. The third band is the multiplier; gold (±5%) and silver (±10%) tolerance bands sit at the end. Preferred E12/E24 values exist so any required value can be made within tolerance.
Power
P = VI = I²R = V²/R. Choose a resistor rated above the calculated dissipation, ideally with margin, and derate with temperature. Wirewound resistors handle the most power; carbon and metal film the least.
Traps
- Read the multiplier band as a power of ten, not as another digit.
- A resistor's power rating is its dissipation limit, not its resistance value.
- Potentiometer = variable voltage divider; rheostat = variable series resistance.
- Conductor resistance changes with temperature - exam questions exploit this.
Worked example
Brown-black-red-gold: 1, 0, x100, ±5% = 1000 Ω ±5% (950-1050 Ω). At 12 V, P = V²/R = 144/1000 = 0.144 W, so a 0.25 W part is adequate.