Current Electricity

विद्युत धारा | Class 12 Physics - Chapter 3 | NCERT + RBSE 2026

This chapter strictly follows NCERT Class 12 Physics textbook and examination pattern for CBSE, RBSE and other state boards

Learning Objectives

After completing this chapter, students will be able to:

• Define electric current and understand its microscopic origin in conductors
• State and apply Ohm's law to solve circuit problems
• Explain drift velocity and its relationship with current
• Understand the origin of resistivity in materials
• Analyze temperature dependence of resistance in conductors and semiconductors
• Calculate electrical energy and power consumed in circuits
• Define EMF and internal resistance of cells
• Analyze combinations of cells in series and parallel
• Apply Kirchhoff's laws to solve complex circuit problems
• Understand and apply the Wheatstone bridge principle

1. Introduction

In Chapters 1 and 2, we studied charges at rest (electrostatics). Now we move to current electricity, which deals with charges in motion. Electric current is the foundation of all electrical and electronic devices we use daily.

Understanding current flow, resistance, and energy transfer is essential for analyzing circuits, designing electronic systems, and solving practical electrical problems.

2. Electric Current

2.1 Definition

Electric current is defined as the rate of flow of electric charge through a conductor.

2.2 Direction of Current

2.3 Types of Current

• Direct Current (DC): Current flows in one direction only (e.g., from batteries)
• Alternating Current (AC): Current periodically reverses direction (e.g., household supply)

3. Electric Currents in Conductors

In a metallic conductor:

• Free electrons undergo random thermal motion (speeds ~ 10⁶ m/s)
• No net current in absence of electric field (random directions cancel)
• When electric field applied: electrons acquire small drift velocity (~10⁻⁴ m/s) superimposed on thermal motion
• This organized drift creates electric current

3.1 Drift Velocity

4. Ohm's Law

Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions (temperature, etc.) remain constant.

4.1 Resistance

Resistance is the property of a conductor that opposes the flow of current.

4.2 Conductance

Conductance is the reciprocal of resistance, measuring ease of current flow.

5. Drift of Electrons and Origin of Resistivity

5.1 Current and Drift Velocity Relationship

5.2 Origin of Resistivity

Resistivity arises from collisions of electrons with:

• Lattice ions (vibrating due to thermal energy)
• Impurities and defects in the crystal structure
• Other electrons

These collisions randomize electron motion, preventing unlimited acceleration and creating resistance to current flow.

6. Mobility

7. Limitations of Ohm's Law

Ohm's law is not a universal law. It has limitations:

Ohmic conductors: Materials that obey Ohm's law (constant R at constant T)

Non-ohmic conductors: Materials that don't obey Ohm's law (R varies with V or I)

8. Resistivity of Various Materials

Material	Resistivity (Ω·m) at 20°C	Type
Silver	1.6 × 10⁻⁸	Conductor (best)
Copper	1.7 × 10⁻⁸	Conductor
Aluminum	2.7 × 10⁻⁸	Conductor
Tungsten	5.6 × 10⁻⁸	Conductor
Iron	10 × 10⁻⁸	Conductor
Nichrome	100 × 10⁻⁸	Alloy (heating element)
Silicon	0.1 to 60	Semiconductor
Glass	10¹⁰ to 10¹⁴	Insulator

9. Temperature Dependence of Resistivity

9.1 Metallic Conductors

Physical explanation: As temperature increases, lattice ions vibrate more vigorously, causing more frequent collisions with electrons, increasing resistivity.

9.2 Semiconductors

For semiconductors:

• Resistivity decreases with increasing temperature (α < 0)
• At higher T, more electrons gain energy to jump to conduction band
• Number of charge carriers increases significantly
• This effect dominates over increased collision rate

9.3 Superconductivity

Some materials show zero resistance below a critical temperature T_c:

• Mercury: T_c = 4.2 K
• Lead: T_c = 7.2 K
• High-temperature superconductors: T_c up to 138 K

10. Electrical Energy and Power

10.1 Electrical Energy

10.2 Electrical Power

11. Cells, EMF, and Internal Resistance

11.1 Electromotive Force (EMF)

11.2 Internal Resistance

Internal resistance (r) is the resistance offered by the electrolyte and electrodes inside the cell.

11.3 Types of Cells

Type	Description	Examples	Reversible?
Primary Cells	Chemical reaction irreversible	Dry cell, Alkaline	No
Secondary Cells	Can be recharged	Lead-acid, Li-ion	Yes

12. Cells in Series and Parallel

12.1 Cells in Series

12.2 Cells in Parallel

13. Kirchhoff's Rules

Kirchhoff's laws are powerful tools for analyzing complex circuits that cannot be simplified using series-parallel combinations.

13.1 Kirchhoff's Current Law (KCL)

13.2 Kirchhoff's Voltage Law (KVL)

13.3 Sign Conventions

14. Wheatstone Bridge

The Wheatstone bridge is a circuit used to measure unknown resistance with high accuracy.

14.1 Principle

Four resistances R₁, R₂, R₃, R₄ are arranged in a bridge configuration with a galvanometer G between points B and C.

14.2 Applications

• Measuring unknown resistance: If three resistances known, fourth can be calculated
• Strain gauges: Measuring small changes in resistance
• Temperature sensors: Using thermistors in bridge circuit
• Meter bridge: Practical implementation using uniform wire

Practice Questions

Multiple Choice Questions (20 MCQs)

Formula Sheet

Concept	Formula	Unit
Current	I = Q/t = dQ/dt	A (Ampere)
Ohm's Law	V = IR	V, A, Ω
Resistance	R = ρL/A	Ω (Ohm)
Current (drift)	I = neAvd	A
Drift velocity	vd = eEτ/me	m/s
Mobility	μ = vd/E = eτ/me	m²/(V·s)
Resistivity (T)	ρT = ρ₀[1 + α(T − T₀)]	Ω·m
Power	P = VI = I²R = V²/R	W (Watt)
Energy	W = Pt = VIt	J (Joule)
Terminal voltage	V = ε − Ir	V
Cells in series	εeq = nε, req = nr	V, Ω
Cells in parallel	εeq = ε, req = r/n	V, Ω
KCL	ΣIin = ΣIout	A
KVL	ΣV = 0 (closed loop)	V
Wheatstone bridge	R₁/R₂ = R₃/R₄	Dimensionless