Conducting and Insulating Materials

Basic Electrical & Electronics Engineering — Basic Concept, NEC licence examination syllabus (Nepal Engineering Council).

Conductors and Insulators: why copper carries and rubber refuses

The answer is in the energy gap, not the material's "hardness".

Why can a copper wire carry current while the plastic wrapped around it carries none, when both are solid matter made of atoms? The real explanation lives in how tightly each material holds its outermost electrons — and this same idea, extended one step, explains semiconductors, which the whole of Section 4 depends on.

The energy-band picture

R = ρL / A With rho = 1.7, L = 100 m, A = 2.5 mm², R = 0.68 Ω.

Doubling the length doubles the resistance; doubling the cross-section halves it. A thicker wire has MORE material and LESS resistance, because the current has more room to pass — which is why long thin cables drop voltage and short fat ones do not.

In a solid, electron energies fall into bands. The valence band holds electrons bound to atoms; the conduction band holds electrons free to drift and form current. The gap between them decides everything.

⚔️ Conductor vs Insulator

ConductorValence and conduction bands overlap, so there is effectively no gap. Huge numbers of free electrons (~10²⁸/m³). Very low resistivity (copper: 1.7 × 10⁻⁸ Ω·m). Resistance increases with temperature — positive temperature coefficient.

InsulatorForbidden gap larger than about 5 eV, so almost no electron gets across at room temperature. Very few free carriers. Very high resistivity (glass: ~10¹² Ω·m). Resistance decreases with temperature — negative coefficient.

SemiconductorGap around 1 eV — an in-between case. Behaves like an insulator when cold and conducts increasingly well as it warms or is doped. This is the whole basis of diodes and transistors.

The temperature behaviour is the giveaway in exam questions. A conductor's resistance rises with heat (atoms vibrate more and obstruct electrons). An insulator's or semiconductor's falls (heat frees more carriers). If a question asks you to identify a material from its temperature response, this is the test.

Typical values worth remembering

Resistivity ρ at 20 °C (Ω·m) Silver 1.6 × 10⁻⁸ best conductor, expensive Copper 1.7 × 10⁻⁸ the practical standard for wiring Aluminium 2.8 × 10⁻⁸ lighter, used for overhead lines Silicon ~6.4 × 10² semiconductor Glass ~10¹² insulator Rubber ~10¹³ insulator

Where each is used, and why

Copper wins for wiring on conductivity-per-rupee. Aluminium wins for long overhead transmission lines despite worse resistivity, because it is far lighter — less sag, cheaper towers. Silver is reserved for contacts and specialised work where its cost is justified. On the insulator side, mica handles heat, PVC wraps household cable, and porcelain holds transmission lines on pylons.

Worked numerical 1 — from material to resistance

The resistivity table above is only useful once you can turn it into an actual resistance. That is what this formula does.

A copper wire is 200 m long with a cross-sectional area of 2.5 mm². Find its resistance at 20 °C.

R = ρL / A ρ = 1.7 × 10⁻⁸ Ω·m (copper, from the table) L = 200 m A = 2.5 mm² = 2.5 × 10⁻⁶ m² ← convert FIRST R = (1.7 × 10⁻⁸ × 200) / (2.5 × 10⁻⁶) = (3.4 × 10⁻⁶) / (2.5 × 10⁻⁶) = 1.36 Ω

The mistake that costs the mark is the area. 1 mm² = 10⁻⁶ m², not 10⁻³ m² — because area is a squared quantity, so the millimetre-to-metre factor of 10⁻³ gets squared too. Convert to metres before substituting, every time.

Worked numerical 2 — what temperature does to it

Earlier we said a conductor's resistance rises when it gets hot. Here is the equation that puts a number on that statement.

Rₜ = R₀ (1 + αt) R₀ = resistance at the reference temperature (usually 20 °C) Rₜ = resistance after the temperature change α = temperature coefficient of resistance (per °C) t = the CHANGE in temperature (°C)

Take the same 1.36 Ω copper wire. On a hot day under load its temperature rises by 50 °C. Copper has α ≈ 0.004 /°C. What is its new resistance?

Rₜ = 1.36 × (1 + 0.004 × 50) = 1.36 × (1 + 0.2) = 1.36 × 1.2 = 1.63 Ω A 20% rise in resistance, from heat alone.

Why does this matter? Higher resistance means more I²R heating for the same current — which raises the temperature further, which raises the resistance again. Cable ratings exist precisely to stop that loop running away.

Sign check — this is the whole point of the topic. For a conductor, α is positive: resistance goes UP with heat. For a semiconductor or insulator, α is negative: resistance goes DOWN with heat. Why the difference? Heating gives more electrons enough energy to cross the forbidden gap, so a semiconductor gains carriers faster than its atoms can obstruct them. If your answer has resistance falling for copper, you have used the wrong sign.

💡 Exam angle: this is usually a short 2–4 mark comparison. Score it by naming the forbidden energy gap, giving a resistivity figure, stating the temperature coefficient's sign, and giving one example material for each class. Four specific facts beat a paragraph of general description.

Syllabus points

Conductors vs insulators

Create a free account to tick topics off, take notes as you read, watch the video lessons and get a day-by-day study plan built around your exam date.