Current Electricity – Class 12 Physics Chapter 3 Notes & NCERT PDF

Introduction

Chapter 3 moves from charges at rest to charges in motion. It explains what electric current is, how Ohm's law arises from the drift of electrons, how resistivity depends on material and temperature, how cells supply energy, and how to analyse circuits with Kirchhoff's rules and the Wheatstone bridge.

Key Concepts

3.2–3.3 Electric current

Current is the rate of flow of charge: I = ΔQ/Δt (for steady current I = q/t). SI unit ampere (A). By convention, current flows in the direction of positive-charge motion — opposite to electron flow in metals. Without a field, free electrons move randomly with no net flow; an applied field produces a net drift.

3.4 Ohm's law

V = IR, where R is the resistance (unit ohm, Ω). R = ρl/A: resistance grows with length and falls with cross-sectional area. ρ is the resistivity (Ω m), a material property. Current density j = I/A, and in vector form E = ρj (or j = σE, σ = 1/ρ = conductivity).

3.5 Drift of electrons — the origin of resistivity

In a field E, each electron accelerates (a = −eE/m) between collisions. Averaging over the relaxation time τ gives the drift velocity v_d = −eEτ/m. Then I = neAv_d, which leads to ρ = m/(ne²τ) — Ohm's law from microscopic physics.

3.6 Limitations of Ohm's law

Ohm's law is not universal: some devices have non-linear V–I graphs, current may depend on the sign of V (diodes), or V may not be a single-valued function of I (e.g. GaAs). These are non-ohmic devices.

3.7–3.8 Resistivity and temperature

Materials range from conductors (ρ ~ 10⁻⁸ Ω m) through semiconductors to insulators (ρ up to 10¹⁴–10¹⁶ Ω m). For metals, ρ_T = ρ₀[1 + α(T − T₀)] with a positive temperature coefficient α. Nichrome has high ρ and a small α (useful in heaters), manganin and constantan have very small α (standard resistors), and semiconductors have ρ decreasing with temperature (negative α).

3.9 Electrical energy and power

Power dissipated: P = VI = I²R = V²/R. Power transmission uses high voltage so that current, and hence line loss I²R_c, is small.

3.10–3.11 Cells, emf and internal resistance

The emf ε is the potential difference between the terminals of a cell on open circuit. With internal resistance r and external resistance R: I = ε/(R + r), and terminal voltage V = ε − Ir.

3.12 Kirchhoff's rules

3.13 Wheatstone bridge

Four resistances R₁, R₂, R₃, R₄ with a galvanometer across the middle. The bridge is balanced (no galvanometer current) when R₂/R₁ = R₄/R₃. This lets an unknown resistance be found accurately from three known ones.

Resistor combinations

Worked Examples

Formula / Key-Facts Sheet

Board Exam Focus

Key Terms

Electric current (विद्युत धारा), Current density (धारा घनत्व), Resistance (प्रतिरोध), Resistivity (प्रतिरोधकता), Conductivity (चालकता), Drift velocity (अपवाह वेग), Relaxation time (विश्रांति काल), Mobility (गतिशीलता), Temperature coefficient (ताप गुणांक), Electromotive force (विद्युत वाहक बल), Internal resistance (आंतरिक प्रतिरोध), Terminal voltage (टर्मिनल विभवांतर), Kirchhoff's rules (किरखोफ के नियम), Wheatstone bridge (व्हीटस्टोन सेतु), Power (शक्ति)

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