Topic 10 — Conductors, Semiconductors & Insulators

Part 1 · The idea, told simply

Hold an ordinary electrical cable. The copper inside carries current happily. The plastic around it carries essentially none. They are touching each other. What makes them so different?

Story track · who is allowed to move

Every material is packed with electrons. The difference is not how many electrons there are — it is how many are free to go anywhere.

In a metal, some electrons have effectively been handed over by their atoms to the whole block of material. They wander through it like people in a public square, and when you apply a field they all drift. Current flows easily.

In an insulator, every electron is held tightly by its own atom, like a person locked in a room. Apply a field and they strain against their bonds, but they cannot travel. NCERT puts it exactly: in some materials the electrons will still be bound, that is, they will not accelerate even if an electric field is applied.

A semiconductor sits between the two. Its electrons are held, but only just — a little heat, or a well-chosen impurity, sets some of them loose.

Animation 1 · Bound, free, and in between

Switch on the field. Watch which electrons move and which merely strain in place.

Part 2 · The resistivity ladder

NCERT §3.7 classifies materials by resistivity, in increasing order of their values: conductors, then semiconductors, then insulators.

Class	Resistivity ρ	Behaviour on heating	Examples
Conductors	10⁻⁸ to 10⁻⁶ Ω m	ρ increases	copper, silver, aluminium
Semiconductors	middle of the range on a log scale	ρ decreases	silicon, germanium
Insulators	10²² to 10²⁴ times the metal values	ρ decreases	glass, rubber, ceramic, plastics

A note on the two numbers NCERT gives — read this, it prevents a marking dispute

The main text of §3.7 says insulators have resistivities 10¹⁸ times greater than metals or more. The Summary (point 5) says glass and rubber have 10²² to 10²⁴ times greater resistivity.

These are not contradictory — the first is a floor ("or more"), the second a typical range for those particular materials. If an exam option offers 10²² to 10²⁴, that is the Summary figure and is the intended answer. Know both, and do not be thrown if a question quotes the other.

Animation 2 · Twenty-four powers of ten

A linear axis is useless here. Click a material to place it on the logarithmic ladder.

Putting the span in perspective

Take a cube of side 1 cm and measure the resistance between opposite faces, using R = ρl/A with l = 0.01 m and A = 10⁻⁴ m²:

Copper cube: R = 1.7 × 10⁻⁸ × 0.01 / 10⁻⁴ ≈ 1.7 × 10⁻⁶ Ω (two millionths of an ohm) Silicon cube: R = 2300 × 0.01 / 10⁻⁴ ≈ 2.3 × 10⁵ Ω (230 kilo-ohms)

The same shape, the same size, the same measurement — and eleven orders of magnitude between them. That is why one formula, R = ρl/A, has to cover wires and insulation alike.

Part 3 · Who carries the current

Story track

It is tempting to assume current always means electrons. In solids it does — but not everywhere.

In a solid conductor, the atoms are locked in a rigid lattice, so they cannot go anywhere. Only the electrons move. NCERT states the picture used throughout the chapter: the current is carried by the negatively charged electrons in the background of fixed positive ions.

In an electrolyte — salt water, a car battery — the ions themselves are free to swim. Positive ions drift one way and negative ions the other. Both motions constitute current in the same direction, so their contributions add.

In an ionised gas, such as the ionosphere in the upper atmosphere, the carriers are electrons and positive ions together. NCERT opens §3.3 by noting that free charged particles do exist in nature, in the upper strata of the atmosphere.

Animation 3 · Three kinds of carrier

Same current direction in all three. Watch what is actually moving in each case.

Maths track · why both ion signs add up

NCERT's Points to Ponder 5 makes this precise. In general the current density has a contribution from each type of carrier:

j = ρ₊v₊ + ρ₋v₋

A positive carrier drifting along E and a negative carrier drifting against E both give a current density along E, because reversing both the sign of the charge and the direction of motion leaves the product unchanged. So the two contributions reinforce rather than cancel.

The same section adds a caution: in a neutral metal wire, ρ₊ = −ρ₋ so the total charge density ρ is zero, and with the positive ions fixed (v₊ ≈ 0) the current density reduces to j = ρ₋v. The naive relation j = ρv applied to the total charge density would wrongly give zero — the relation must be applied to each carrier type separately.

Part 4 · Why semiconductors are the useful ones

Story track

A copper wire is a good conductor and will always be a good conductor. A glass rod is an insulator and will always be an insulator. Neither can be persuaded to change its mind, and that makes them dull.

A semiconductor can be tuned. Add a tiny amount of a suitable impurity — a process called doping — and its resistivity drops dramatically, because the impurity supplies extra charge carriers. Change the impurity and you change the material's electrical character.

NCERT states the consequence in one sentence: this last feature is exploited in the use of semiconductors for electronic devices. Every transistor and every chip exists because of it.

ρ = m/(n e² τ) doping raises n ⇒ ρ falls

Note that this is the same variable that governs the temperature behaviour from Topic 9. Semiconductors respond strongly to heating and to doping for one shared reason: in a semiconductor, n is something you can change.

Animation 4 · Doping a semiconductor

Add impurity atoms one at a time. Each contributes a carrier — and the resistivity falls fast.

doping level =

Conductivity: the same information, upside down

σ = 1/ρ unit: siemens per metre, S m⁻¹ j = σE Good conductor → small ρ, LARGE σ Good insulator → large ρ, small σ

Keep the pair straight against the object-level pair from Topic 4: ρ and σ describe the material; R and G describe the particular object.

Animation 5 · Resistivity and conductivity, back to back

Two ways of saying the same thing. As one bar grows, the other shrinks — and the ordering of materials reverses.

log₁₀ ρ =

Trap · the six that cost marks

Ranking the classes by resistance instead of resistivity. A thin copper wire can out-resist a thick block of anything.
Saying semiconductors have α positive. Their resistivity FALLS on heating.
Assuming current always means electrons. In electrolytes both ion signs move and both contribute.
Thinking the two ion contributions cancel. They add, because charge sign and drift direction both reverse.
Applying j = ρv to the total charge density in a wire. It must be applied to each carrier type separately.
Confusing conductance (per object, S) with conductivity (per material, S m⁻¹).

Part 5 · Formula sheet

Classification (NCERT §3.7)

Order of increasing resistivity: conductors < semiconductors < insulators Metals: ρ ≈ 10⁻⁸ to 10⁻⁶ Ω m Insulators: 10²² to 10²⁴ times metal values (Summary) "10¹⁸ times or more" (main text) Semiconductors: middle of the range on a LOG scale Total span of matter: about 10²⁴, the widest of any common property

Sign of the temperature response

Conductors α positive → ρ rises on heating Alloys α ≈ 0 → ρ nearly constant (standard resistors) Semiconductors α negative → ρ falls on heating Insulators α negative → ρ falls on heating Mechanism: metals limited by τ · semiconductors driven by n

Carriers of current

Solid conductors: electrons only, in a background of FIXED positive ions Electrolytes: both positive and negative ions move; contributions ADD Ionised gas: electrons and positive ions Ionosphere: naturally occurring free charged particles Insulators: electrons bound; they do not accelerate in a field

Conductivity and current density

σ = 1/ρ unit S m⁻¹ j = σE (local form of Ohm's law) σ = n e² τ/m = n e μ j = ρ₊v₊ + ρ₋v₋ apply to EACH carrier type separately In a neutral wire: ρ₊ = −ρ₋, v₊ ≈ 0, so j = ρ₋v

Doping

Adding a small amount of a suitable impurity RAISES n ρ = m/(ne²τ) therefore FALLS This tunability is why semiconductors are used in electronic devices Geometry (l, A) never changes ρ — only material, temperature, pressure, doping

Sanity checks

ρ is a MATERIAL property · R is an OBJECT property σ is per metre (S m⁻¹) · G is per object (S) A good conductor has small ρ and large σ The three classes are ordered by ρ, never by R Doping lowers resistivity; it never raises it

Part 6 · 50 NEET-pattern questions with full solutions

Includes 4 graph-based questions, 3 assertion–reason questions, and 9 questions tagged Carriers on what actually moves in each material. Year labels are not attached: the patterns are authentic, the wording is mine.