Alternating Current Class 12 Notes | CBSE Physics Chapter 7

Alternating Current is Chapter 7 of CBSE Class 12 Physics. This chapter covers AC circuits containing resistors, inductors, and capacitors (RLC circuits), the concept of impedance, resonance, power in AC circuits, and transformers. Understanding AC is essential since household electricity in India is AC at 220 V, 50 Hz.

This chapter carries 5–7 marks. LCR circuit analysis, resonance, transformer problems, and power factor are commonly tested.

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Key Concepts

1. Alternating Current Basics

An alternating current changes direction periodically. It is described as:

I = I₀ sin ωt and V = V₀ sin ωt

where I₀, V₀ are peak values and ω = 2πf (angular frequency).

RMS (Root Mean Square) Values

The effective or DC-equivalent values used for AC calculations:

Irms = I₀/√2 ≈ 0.707 I₀

Vrms = V₀/√2 ≈ 0.707 V₀

Household AC: Vrms = 220 V → V₀ = 220√2 ≈ 311 V

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2. AC Through Pure Components

Component	Impedance	Phase Relation
Resistor (R)	R	V and I are in phase
Inductor (L)	XL = ωL = 2πfL	V leads I by 90° (π/2)
Capacitor (C)	XC = 1/(ωC) = 1/(2πfC)	I leads V by 90° (π/2)

XL = inductive reactance; XC = capacitive reactance (both in Ω)

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3. Series LCR Circuit

Impedance: Z = √[R² + (XL − XC)²]

Current: I = V/Z

Phase angle: tan φ = (XL − XC)/R

• If XL > XC: circuit is inductive (V leads I)
• If XC > XL: circuit is capacitive (I leads V)
• If XL = XC: resonance (purely resistive)

Resonance

At resonance: XL = XC → ωL = 1/(ωC)

Resonant frequency: f₀ = 1/(2π√LC)

At resonance: Z = R (minimum impedance), I = V/R (maximum current)

Quality Factor (Q)

Q = ωL/R = 1/(ωCR) = (1/R)√(L/C)

Higher Q → sharper resonance peak → more selective tuning

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4. Power in AC Circuits

P = VrmsIrms cos φ

where cos φ is the power factor.

Circuit	Power Factor	Power
Pure R	cos φ = 1	P = VI (maximum)
Pure L or C	cos φ = 0	P = 0 (wattless current)
LCR at resonance	cos φ = 1	P = V²/R (maximum)

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5. Transformer

A device that changes AC voltage from one level to another using mutual induction.

Vs/Vp = Ns/Np = Ip/Is (for ideal transformer)

• Step-up: Ns > Np → voltage increases, current decreases
• Step-down: Ns < Np → voltage decreases, current increases
• Efficiency: η = (output power)/(input power) × 100%. Ideal transformer: η = 100%

Energy Losses in Transformer

• Copper loss: I²R heating in coils → use thick copper wires
• Iron/core loss: Eddy currents in core → use laminated core
• Hysteresis loss: Energy to magnetise/demagnetise core each cycle → use soft iron
• Flux leakage: Not all flux links both coils → use close winding

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Solved Examples

Example 1

A series LCR circuit has R = 100 Ω, L = 0.5 H, C = 10 μF connected to 200 V, 50 Hz. Find impedance and current.

Answer: XL = 2π × 50 × 0.5 = 157 Ω. XC = 1/(2π × 50 × 10⁻⁵) = 318 Ω.

Z = √[100² + (157 − 318)²] = √[10000 + 25921] = √35921 = 189.5 Ω

I = V/Z = 200/189.5 = 1.06 A

Example 2

Find the resonant frequency for L = 0.1 H and C = 100 μF.

Answer: f₀ = 1/(2π√LC) = 1/(2π√(0.1 × 10⁻⁴)) = 1/(2π × 3.16 × 10⁻³) = 50.3 Hz

Example 3

A transformer with 500 primary turns and 50 secondary turns is connected to 220 V AC. Find the output voltage.

Answer: Vs = Vp × Ns/Np = 220 × 50/500 = 22 V (step-down)

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Important Questions for Board Exams

1-Mark

1. What is the power factor of a pure inductor?
2. What is resonance in an LCR circuit?

3-Mark

1. Derive the expression for impedance of a series LCR circuit.
2. What is a transformer? Explain its working with a diagram.
3. What is resonance? Derive the condition and resonant frequency for a series LCR circuit.

5-Mark

1. Explain the working of a series LCR circuit. Derive expressions for impedance and resonant frequency. What is the Q factor?

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Quick Revision Points

• AC: I = I₀ sin ωt; Irms = I₀/√2; Vrms = V₀/√2
• XL = ωL (V leads I by 90°); XC = 1/(ωC) (I leads V by 90°)
• LCR: Z = √[R² + (XL − XC)²]; tan φ = (XL − XC)/R
• Resonance: XL = XC; f₀ = 1/(2π√LC); Z = R (min); I = max
• Power: P = VIcos φ; pure L or C → P = 0 (wattless)
• Transformer: Vs/Vp = Ns/Np; losses: copper, iron, hysteresis, flux leakage

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Previous: Ch 6 — Electromagnetic Induction
Next: Ch 8 — Electromagnetic Waves