Current Electricity – Stage 1 (Concept Strengthening)

Page 5: Ohm’s Law – Macroscopic & Microscopic View

1️⃣ Ohm’s Law (Macroscopic Form)

Ohm’s Law states that current through a conductor is directly proportional to the potential difference across it, provided physical conditions remain constant.

Formula:
V = IR

  • V → Potential difference
  • I → Current
  • R → Resistance

This is a macroscopic law — it does not explain what happens inside the conductor.

2️⃣ Conditions for Validity of Ohm’s Law

  • Temperature must be constant
  • Physical dimensions unchanged
  • Material must be ohmic

⚠️ JEE Trap:
Ohm’s law fails for diodes, electrolytes, thermistors.

3️⃣ Microscopic Form of Ohm’s Law

At microscopic level, Ohm’s law is expressed in terms of electric field and current density.

Microscopic Relation:
J = σE

  • J → Current density
  • E → Electric field
  • σ → Electrical conductivity

4️⃣ Electrical Conductivity (σ)

Conductivity depends on material properties:

σ = nq²τ / m

  • n → Number density of electrons
  • q → Charge of electron
  • τ → Relaxation time
  • m → Mass of electron

Higher τ → higher conductivity → lower resistance.

5️⃣ Relation Between E and Drift Velocity

Electric field causes drift of electrons:

vd = qEτ / m

Thus electric field is the real cause of current.

6️⃣ Linking All Relations (JEE Favorite)

  • J = nqvd
  • vd ∝ E
  • ∴ J ∝ E

Hence:
Ohm’s law emerges from microscopic charge motion.

7️⃣ Comparison Table

Macroscopic Microscopic
V = IR J = σE
Deals with circuit quantities Deals with charge motion
No material insight Explains material behavior

8️⃣ IIT/JEE Thinking Insight

Key Idea:
Resistance is not just opposition — it is the result of electron collisions.

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