Resistance and Resistors
Resistance and resistors questions test the dependence of resistance on material and dimensions, resistor identification, and temperature effects. You must use R = ρL/A, read colour codes, and select appropriate resistor ratings.
Core rules
- R = ρL/A: resistance rises with length and resistivity, and falls with cross-sectional area.
- Resistivity ρ is a material property measured in ohm-metres; resistance is measured in ohms.
- Metal resistance generally rises with temperature; negative-temperature-coefficient thermistors fall in resistance as they warm.
- Series resistances add; parallel resistances combine by reciprocals.
- Colour bands give value and tolerance; a four-band resistor uses two value digits, a multiplier, and tolerance.
- Resistors have a power rating; exceeding it causes overheating and drift.
Worked example
Find the resistance of a 2.0 m copper wire of cross-sectional area 1.0 mm². Take ρ = 1.7 × 10^-8 Ω·m. Convert area: 1.0 mm² = 1.0 × 10^-6 m². R = ρL/A = (1.7 × 10^-8 × 2.0) / (1.0 × 10^-6) = 0.034 Ω. Reasoning: convert area to square metres before substituting; otherwise the result is wrong by a factor of a million.
Traps
- Using diameter where area is required.
- Thinking thicker wire has higher resistance; it has lower resistance.
- Confusing resistivity with resistance.
- Ignoring tolerance bands and power rating when choosing a resistor.