Current Electricity - Electrical Conductivity
current electricity electrical conductivity is explained with formula sheets, derivations, conductivity vs resistivity, drift velocity, mobility, conductors, semiconductors, temperature dependence, SVG graphs and exam-level practice for CBSE Class 12, NEET, JEE Main, JEE Advanced, AP, IB, IGCSE, A-Level and Olympiad Physics.
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1. Formula Sheet First
σ = 1/ρConductivity is reciprocal of resistivity.ρ = 1/σResistivity is reciprocal of conductivity.σ = neμConductivity using mobility.σ = ne²τ/mDrude model expression.J = σEMicroscopic Ohm's law.E = ρJResistive form.vd = μEDrift velocity and mobility.μ = vd/EDefinition of mobility.ρ = m/(ne²τ)Microscopic resistivity.[σ] = S m-1SI unit of conductivity.[σ] = M⁻¹L⁻³T³A²Dimensional formula.[μ] = m²V⁻¹s⁻¹SI unit of mobility.Symbols: σ = conductivity, ρ = resistivity, n = free electron density, e = electronic charge, μ = mobility, τ = relaxation time, m = electron mass, J = current density, E = electric field, vd = drift velocity.
Core idea: High conductivity means charges move easily through a material. Low conductivity means current flow is difficult.
2. What Is Electrical Conductivity?
Electrical conductivity is a material property that measures how easily electric current can flow through a substance. It is high for good conductors, moderate for semiconductors and very low for insulators.
Conductivity vs conductance: Conductivity is material property; conductance belongs to a particular object or wire.
Conductivity vs resistivity: They are reciprocal. If conductivity is high, resistivity is low.
Physical significance: Conductivity depends on carrier density, charge, mobility and relaxation time.
3. Conductivity vs Resistivity
| Material | Conductivity | Resistivity | Use |
|---|---|---|---|
| Silver | Very high | Very low | Special contacts. |
| Copper | High | Low | Electrical wiring. |
| Aluminium | High | Low | Transmission cables. |
| Nichrome | Low | High | Heating elements. |
| Manganin | Low/moderate | High | Resistance boxes. |
| Germanium/Silicon | Moderate, temperature dependent | Moderate | Semiconductors. |
| Glass/Rubber | Very low | Very high | Insulation. |
4. Derivation of σ = 1/ρ
1
For a wire, R = ρL/A.
2
Conductance is reciprocal of resistance: G = 1/R.
3
So G = A/(ρL).
4
But conductance of a conductor can be written as G = σA/L.
5
Comparing both expressions gives σ = 1/ρ.
5. Derivation of σ = ne²τ/m
1
Drift velocity is vd = eEτ/m.
2
Current density is J = nevd.
3
Substitute vd to get J = ne²τE/m.
4
Compare with J = σE.
5
Therefore σ = ne²τ/m.
6-7. Conductivity and Mobility
1
Mobility is μ = eτ/m.
2
Substitute μ into σ = ne²τ/m.
3
So σ = neμ.
Higher mobility: charges drift more easily, so conductivity increases.
Lower mobility: more scattering reduces conductivity.
Semiconductors: both electrons and holes contribute to total conductivity.
8. Conductivity and Drift Velocity
Conductivity connects microscopic charge motion to macroscopic current. Since J = nevd and vd = μE, we get J = neμE, so σ = neμ.
Free electron density: more carriers usually increase conductivity.
Electric field: field drives drift motion.
Mobility: measures how easily carriers respond to the field.
9. Temperature Dependence of Conductivity
| Material | When Temperature Increases | Conductivity | Resistivity |
|---|---|---|---|
| Metals | Lattice vibration increases and relaxation time decreases. | Decreases. | Increases. |
| Semiconductors | Carrier concentration increases strongly. | Increases. | Decreases. |
10. Best and Worst Conductors
Excellent conductors: silver, copper, gold and aluminium.
Moderate conductors: iron and steel.
Poor conductors: nichrome and manganin.
Insulators: glass, rubber and plastic.
Applications: copper wires, aluminium cables, nichrome heaters, rubber insulation.
Exam point: best conductor is not always used practically because cost, strength and oxidation also matter.
11. Graphs and SVG Diagrams
12-18. Exam Question Bank With Accordion Solutions
Click any question to open the answer and explanation.
19. Common Student Mistakes
20. Final Revision Sheet
Core formulas: σ = 1/ρ, σ = neμ, σ = ne²τ/m.
Current density: J = σE and J = nevd.
Mobility: μ = vd/E = eτ/m.
Metals: temperature increases, conductivity decreases.
Semiconductors: temperature increases, conductivity increases.
Exam trick: J-E graph slope gives conductivity.
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