Tamil Nadu Class 12 Physics — Current Electricity (Samacheer Kalvi)

Quick Summary

Current electricity deals with the flow of electric charges through conductors and the laws governing circuits. This chapter carries 8–10 marks in the TN HSE board exam and is highly relevant for NEET and JEE (Ohm's law, Kirchhoff's laws, and Wheatstone bridge questions appear regularly).

Key Concepts and Definitions

• Electric Current (I): Rate of flow of charge. I = Q/t (Amperes)
• Current Density (J): Current per unit cross-sectional area. J = I/A
• Drift Velocity (vd): Average velocity of electrons under electric field
• Resistivity (ρ): Property of material opposing current flow
• EMF: Work done per unit charge by a source; ε = W/q
• Internal Resistance (r): Resistance within the battery itself

Formulae

Drift Velocity and Current

Free electrons in a conductor have random thermal motion. When an electric field E is applied, electrons acquire a net drift in the opposite direction to E.

vd = eEτ/m

Where:

• e = charge of electron (1.6 × 10⁻¹⁹ C)
• τ = relaxation time (~10⁻¹⁴ s)
• m = mass of electron (9.1 × 10⁻³¹ kg)

The relation between current and drift velocity:

I = nAevd

Where n = number density of free electrons.

Ohm's Law and Resistance

Ohm's Law: V = IR (valid for ohmic conductors at constant temperature)

Resistivity: R = ρl/A

• ρ depends on material and temperature
• ρ increases with temperature for metals: ρ(T) = ρ₀[1 + α(T − T₀)]
• α = temperature coefficient of resistance

Colour Code for Resistors: B B ROY of Great Britain Very Good Wife — Black(0), Brown(1), Red(2), Orange(3), Yellow(4), Green(5), Blue(6), Violet(7), Grey(8), White(9)

Kirchhoff's Laws

KCL (Junction Rule)

At any junction, the sum of incoming currents = sum of outgoing currents.

ΣI_in = ΣI_out or ΣI = 0

Based on conservation of charge.

KVL (Loop Rule)

Around any closed loop, the algebraic sum of all potential differences is zero.

ΣV = 0 or Σ(IR) = ΣEMF

Based on conservation of energy.

Wheatstone Bridge

Four resistors P, Q, R, S arranged in a diamond. A galvanometer G connects the midpoints.

Balanced condition: P/Q = R/S → no current through G

Meter Bridge is a practical application:

• L/(100 − L) = R/S
• Unknown resistance: X = R(100 − L)/L

Potentiometer

A long resistance wire used to measure EMF and internal resistance accurately.

Principle: Potential drop across a wire ∝ its length (uniform cross-section and current).

Comparing EMFs: ε₁/ε₂ = l₁/l₂

Finding internal resistance: r = R(l₁ − l₂)/l₂

Important Questions

One Mark

1. Define drift velocity. 2. State Ohm's Law. 3. What is the condition for balance in a Wheatstone bridge? 4. Define resistivity and give its SI unit. 5. What is the principle of a potentiometer?

Short Answer (3 marks)

1. Derive the expression for drift velocity and relate it to current density. 2. State and explain Kirchhoff's laws with examples. 3. Describe the working of a metre bridge with a circuit diagram.

Long Answer (5 marks)

1. Explain the Wheatstone bridge principle and derive the balance condition. Describe how a metre bridge works as a practical Wheatstone bridge. 2. Describe the potentiometer principle. Explain how it is used to (a) compare EMFs of two cells and (b) find the internal resistance of a cell.

Board Exam Tips

• Draw neat, labelled circuit diagrams — they carry marks
• For KVL, always specify the direction of traversal in a loop
• Meter bridge formula L/(100 − L) = R/X — memorise it
• "Sensitive galvanometer" — know it means small current detection
• Numericals on power dissipation (P = I²R) are very common

Revision Checklist

• [ ] Define and derive drift velocity
• [ ] Solve KCL and KVL circuit problems
• [ ] Draw and explain Wheatstone bridge circuit
• [ ] Derive balance condition for Wheatstone bridge
• [ ] Explain metre bridge working
• [ ] Explain potentiometer applications (EMF comparison, internal resistance)
• [ ] Temperature dependence of resistance

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