Current Electricity – Stage 1 (Concept Mastery)

Page 6: Resistance, Resistivity & Temperature Dependence

1️⃣ Resistance (R)

Resistance is the opposition offered by a conductor to the flow of electric current.

Formula:
R = V / I

Resistance depends on:

  • Length of conductor
  • Cross-sectional area
  • Nature of material
  • Temperature

2️⃣ Dependence of Resistance on Dimensions

R ∝ L
R ∝ 1/A

Combining both:

R = ρ L / A

  • L → Length
  • A → Area of cross-section
  • ρ → Resistivity

3️⃣ Resistivity (ρ)

Resistivity is an intrinsic property of a material.

  • Independent of shape and size
  • Depends only on material & temperature

Units:
Ohm-meter (Ω·m)

4️⃣ Temperature Dependence of Resistance (Conductors)

For metallic conductors, resistance increases with temperature.

RT = R0 (1 + αΔT)

  • R0 → Resistance at reference temperature
  • α → Temperature coefficient of resistance

For metals: α > 0

5️⃣ Temperature Dependence (Semiconductors)

For semiconductors:

  • Resistance decreases with temperature
  • α is negative

⚠️ JEE Trap:
Never apply metallic temperature formula to semiconductors.

6️⃣ Superconductors

At a critical temperature (Tc), resistance becomes zero.

  • No energy loss
  • Perfect diamagnetism

7️⃣ Microscopic Meaning of Temperature Effect

As temperature increases:

  • Lattice vibrations increase
  • Electron collision frequency increases
  • Relaxation time (τ) decreases
  • Hence resistance increases

8️⃣ Comparison Table (High-Yield)

Quantity Depends On Independent Of
Resistance (R) L, A, material, temperature —
Resistivity (ρ) Material, temperature L, A

9️⃣ IIT/JEE Thinking Insight

Key Insight:
Resistivity reflects atomic-level scattering, not circuit design.

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