A conductor contains charge carriers that are free to move; copper and aluminium are the usual choices for wiring because they combine low resistivity with mechanical workability. An insulator holds its charges tightly, which is why it is used around conductors. A semiconductor sits between the two and its conductivity can be controlled, which is the basis of diodes and transistors.
Resistance of a conductor
For a uniform conductor at a given temperature, resistance grows with length and falls as cross-sectional area grows. The material property that links them is resistivity.
Copper wire resistance
Problem. A copper conductor is 20 m long with a cross-section of 1.5 mm². Use ρ = 1.72 × 10⁻⁸ Ω·m. Estimate its resistance.
Solution. A = 1.5 mm² = 1.5 × 10⁻⁶ m². R = (1.72 × 10⁻⁸ × 20) ÷ (1.5 × 10⁻⁶) = 0.229 Ω, approximately 0.23 Ω.
Open, closed and short circuits
A closed circuit has a continuous path from the source through the load and back. An open circuit breaks that path, so current stops. A short circuit provides a very low-resistance path around the intended load, so current can rise sharply and the source, wiring or protective device is stressed.
- Closed circuit: normal current flows through the intended load.
- Open circuit: no current flows; the full source voltage appears across the break.
- Short circuit: current bypasses the load and is limited mainly by source and wiring resistance.
- A partial short or high-resistance joint behaves like extra resistance in series and causes heat and voltage drop.
- Copper and aluminium are common conductors; insulation keeps current on its intended path.
- Conductor resistance rises with length and falls with cross-sectional area.
- An open circuit stops current; a short circuit bypasses the load.
- A high-resistance joint causes voltage drop and local heating.
Worked example
A 2.5 mm² aluminium conductor has a higher resistivity than copper, so for the same length and current it drops more voltage and dissipates more heat. That is why the material, length, cross-section and current must be considered together when a circuit is designed.