Conducting materials
A conductor has many free electrons. Its resistivity (ρ) is very small. Resistance of a wire is R = ρ L / A (L is length, A is cross-section area).
- Copper (ρ ≈ 1.7 × 10−8 Ω·m): the best common choice for wires and windings.
- Aluminium (ρ ≈ 2.8 × 10−8 Ω·m): lighter and cheaper, used in overhead lines.
- Nichrome and tungsten: high resistivity and survive heat, so they make heater elements and lamp filaments.
- Solder and fuse wire: low melting point, so they join parts or cut the current.
Metals get more resistive when hot, because the atoms shake more and block the electrons.
Insulating materials
An insulator has almost no free electrons. Its resistivity is huge (glass can be 1010 Ω·m or more). It keeps current where it should be and keeps people safe.
Every insulator has a limit. Dielectric strength is the largest electric field (in kV per mm) it can take. Beyond it comes breakdown: a spark, and the insulator is damaged. Air is about 3 kV/mm; good solid insulators are much higher.
- Solids: porcelain and glass (line insulators), rubber and PVC (wire coat), mica (heaters), paper and varnish (windings).
- Liquids: transformer oil insulates and cools.
- Gases: air, and SF6 in switchgear.
Heat ages insulation. Insulation is graded by the highest temperature it can take, so a motor does not burn out.
Magnetic materials: soft and hard
Inside iron are tiny regions called domains, each like a little magnet. A magnetic field lines them up. Two traits decide use:
- Retentivity: how much magnetism is kept after the field is removed.
- Coercivity: how big a reverse field is needed to wipe it out.
Soft magnetic materials (soft iron, silicon steel, ferrite) have low retentivity and low coercivity. They magnetise and demagnetise easily, with little energy lost as heat on each cycle. Used for transformer and motor cores, relays and electromagnets.
Hard magnetic materials (carbon steel, alnico, neodymium alloys) have high retentivity and high coercivity. They are hard to demagnetise. Used for permanent magnets in speakers, meters and small motors.
The loop of magnetisation against field is the hysteresis loop. Its area is the energy lost each cycle: thin loop for soft, fat loop for hard.
Try it: test the materials
Open the 3D. Press Conductor and drag the voltage slider. Predict: double the voltage, will electrons go twice as fast? Check it. Press Insulator and slide to 100: at what voltage does the spark appear? (Slider 80.)
Press Soft magnet and slide the field up, then back to zero. Do the arrows stay aligned? Repeat with Hard magnet: push past 6 first. At home, rub a steel needle on a magnet and see that it picks up a pin; a soft iron nail loses it quickly.
Key formulas and definitions
- R = ρ L / A
- ρ (copper) ≈ 1.7 × 10⁻⁸ Ω·m; ρ (aluminium) ≈ 2.8 × 10⁻⁸ Ω·m; ρ (nichrome) ≈ 1.1 × 10⁻⁶ Ω·m
- Breakdown voltage ≈ dielectric strength × thickness (kV/mm × mm)
- Air dielectric strength ≈ 3 kV/mm
- Hysteresis loop area = energy lost per cycle
Worked examples
1. A copper wire is 100 m long with area 1.7 mm². Find its resistance. (ρ = 1.7 × 10⁻⁸ Ω·m)
A = 1.7 × 10⁻⁶ m². R = ρ L / A = 1.7 × 10⁻⁸ × 100 / 1.7 × 10⁻⁶ = 1 Ω.
2. A nichrome heater wire has L = 1 m, A = 0.1 mm², ρ = 1.1 × 10⁻⁶ Ω·m. Find R.
A = 1 × 10⁻⁷ m². R = 1.1 × 10⁻⁶ × 1 / 1 × 10⁻⁷ = 11 Ω.
3. An air gap is 2 mm. At what voltage does it break down? (3 kV/mm)
3 kV/mm × 2 mm = 6 kV.
4. An insulating sheet of 0.5 mm has dielectric strength 20 kV/mm. What voltage can it hold?
20 × 0.5 = 10 kV.
5. Which material suits a transformer core: soft iron or hard steel? Why?
Soft iron or silicon steel. The core is magnetised and demagnetised 50 times a second, so low retentivity means a thin loop and little heat loss.
6. Which is better for an overhead line, copper or aluminium?
Aluminium is often used: it is light and cheap, so one thick wire can span long distances. Copper conducts better per area but is heavy and costly.
Common mistakes
- Thinking an insulator never conducts. Above its breakdown voltage it does, and it is damaged.
- Mixing up soft and hard magnets. "Soft" means easy to demagnetise, not weak or squashy.
- Using mm² directly in R = ρL/A. Convert: 1 mm² = 10⁻⁶ m².
- Forgetting heat. Metals get more resistive when hot; insulators age faster when hot.