Tamil Nadu Class 12 Physics — Electromagnetic Induction and Alternating Current (Samacheer Kalvi)

Quick Summary

Electromagnetic induction explains how changing magnetic flux generates EMF — the principle behind generators, motors, and transformers. AC circuits with R, L, C components are central to this chapter. Weightage: 8–10 marks in TN HSE. Highly relevant for JEE (LCR circuits, resonance) and NEET (transformer, generator principles).

Key Concepts and Definitions

• Magnetic Flux (Φ): Φ = BA cosθ (Weber)
• Induced EMF: ε = −dΦ/dt (Faraday's law)
• Self-inductance (L): Property of a coil opposing change in its own current; ε = −L(dI/dt)
• Mutual inductance (M): EMF induced in coil 2 due to changing current in coil 1; ε₂ = −M(dI₁/dt)
• Reactance: Opposition to AC by capacitor (Xc) or inductor (XL)
• Impedance (Z): Total opposition to AC in a circuit

Formulae

Faraday's Laws and Lenz's Law

Faraday's First Law: EMF is induced whenever magnetic flux through a circuit changes.

Faraday's Second Law: Induced EMF ε = −N × dΦ/dt

Lenz's Law: The induced current opposes the cause producing it (negative sign in Faraday's law).

Motional EMF

When a conductor of length l moves with velocity v perpendicular to a field B: ε = Blv

Self-Inductance and Mutual Inductance

Self-inductance: A coil has self-inductance L if ε = −L(dI/dt)

For a solenoid: L = μ₀n²Al (n = turns per unit length, A = area, l = length)

Mutual inductance: Two coils have mutual inductance M if ε₂ = −M(dI₁/dt)

Coefficient of coupling: k = M/√(L₁L₂) (0 ≤ k ≤ 1)

AC Circuits

AC source: V = V₀ sinωt, where ω = 2πf

Pure R circuit: I and V in phase. Power = V_rms × I_rms

Pure L circuit: Current lags voltage by 90°. XL = ωL. Power = 0 (no energy dissipated)

Pure C circuit: Current leads voltage by 90°. XC = 1/ωC. Power = 0

LCR Series Circuit

Impedance: Z = √(R² + (XL − XC)²)

Phase angle: tan φ = (XL − XC)/R

Resonance: When XL = XC → Z = R (minimum), current is maximum

Resonance frequency: f₀ = 1/(2π√LC)

Q-factor (sharpness): Q = ω₀L/R = 1/(ω₀CR)

Transformer

Based on mutual induction. Changes AC voltage.

V₁/V₂ = N₁/N₂ (turns ratio)

For ideal transformer (100% efficiency): V₁I₁ = V₂I₂

• Step-up: N₂ > N₁ → V₂ > V₁
• Step-down: N₂ < N₁ → V₂ < V₁

Losses: Eddy currents (copper core laminated), hysteresis, flux leakage, copper loss

Important Questions

One Mark

1. State Lenz's law. 2. What is resonance in an LCR circuit? 3. Give the formula for inductive reactance. 4. What is the Q-factor of an LCR circuit? 5. Why is transformer core laminated?

Short Answer (3 marks)

1. Derive the expression for motional EMF of a conductor moving in a magnetic field. 2. Explain the construction and working of a transformer. Mention sources of energy loss. 3. Derive the condition for resonance in an LCR series circuit and find the resonance frequency.

Long Answer (5 marks)

1. Explain self-inductance and mutual inductance. Derive the expression for the inductance of a solenoid. 2. Analyse an LCR series circuit connected to an AC source. Derive expressions for impedance, phase angle, and average power. Define power factor.

Board Exam Tips

• Lenz's law diagram — always draw the coil + approaching magnet with arrow showing induced current direction
• Power factor: P = V_rms I_rms cos φ — note cos φ = R/Z
• "Wattless current" = current in pure L or C circuit — zero average power
• Transformer: primary vs secondary — N₁ turns connects to input, N₂ to output

Revision Checklist

• [ ] State and apply Faraday's and Lenz's laws
• [ ] Derive motional EMF
• [ ] Define self-inductance and mutual inductance
• [ ] Analyse pure R, L, C AC circuits
• [ ] Derive impedance and phase angle for LCR circuit
• [ ] Explain resonance and Q-factor
• [ ] Derive transformer equation and state energy losses

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