Alternating Current Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 7 notes: RMS values, AC through R, L and C, reactance and impedance, series LCR resonance, power factor and the transformer.
Alternating Current — Class 12 Physics Notes
Chapter Snapshot
Alternating current reverses direction periodically. This chapter covers how to describe AC (RMS values), how resistors, inductors and capacitors each respond to it (phase relations and reactance), the series LCR circuit with its impedance and resonance, power and power factor, and the transformer.
Board relevance: part of the ~8-mark EMI+AC unit. Expect an LCR impedance/resonance numerical and a transformer question. The phase relations (ELI the ICE man) are the key to avoiding sign mistakes.
Key Concepts & Definitions
AC voltage and current: V = V₀ sin ωt, I = I₀ sin(ωt ± φ), where V₀, I₀ are peak values and ω = 2πf.
RMS (root mean square) value — the equivalent DC value that produces the same heating effect:
Irms = I₀/√2 ≈ 0.707 I₀ ; Vrms = V₀/√2
AC ammeters and voltmeters read RMS values. India's mains "220 V, 50 Hz" means Vrms = 220 V (so V₀ ≈ 311 V) at f = 50 Hz.
Average value over a full cycle is zero for a sinusoidal AC — which is why RMS is used.
Formulas — AC Through R, L and C
Element Phase relation Opposition
Resistor R V and I in phase R
Inductor L Current lags V by 90° XL = ωL = 2πfL
Capacitor C Current leads V by 90° XC = 1/ωC = 1/2πfC
Memory aid — "ELI the ICE man": in an inductor (L), E (voltage) leads I; in a capacitor (C), I leads E.
- XL increases with frequency (an inductor blocks high frequencies); XC decreases with frequency (a capacitor blocks DC, passes high frequencies).
Series LCR circuit
Impedance Z = √(R² + (XL − XC)²) ; Irms = Vrms/Z
Phase angle: tan φ = (XL − XC)/R
- If XL XC the circuit is inductive (current lags); if XC XL it is capacitive (current leads).
Resonance
At resonance XL = XC, so:
ω₀ = 1/√(LC) , f₀ = 1/(2π√(LC))
- Impedance is minimum (Z = R) and current is maximum (I = V/R).
- The circuit is purely resistive (φ = 0). Used for tuning radios to a station.
Power in AC
P = Vrms Irms cos φ
cos φ = R/Z is the power factor.
- Pure R: cos φ = 1 (maximum power).
- Pure L or C: φ = 90°, cos φ = 0 → no power consumed; the current is called a wattless current.
- At resonance cos φ = 1.
Transformer
Changes AC voltage using mutual induction between a primary and secondary coil on a common laminated core.
Vs/Vp = Ns/Np = Ip/Is
- Step-up: Ns Np (voltage up, current down). Step-down: Ns < Np.
- An ideal transformer conserves power: Vp Ip = Vs Is. It works only on AC, not DC.
- Losses: copper loss (I²R heating), eddy currents (reduced by laminating the core), hysteresis (soft-iron core), and flux leakage.
Worked Examples
Example 1 — RMS: An AC source has peak voltage 311 V. Find Vrms.
Vrms = V₀/√2 = 311/1.414 ≈ 220 V.
Example 2 — Reactance: Find XL for L = 0.5 H at 50 Hz.
XL = 2πfL = 2π(50)(0.5) ≈ 157 Ω.
Example 3 — Impedance: A series LCR has R = 30 Ω, XL = 40 Ω, XC = 80 Ω. Find Z and the phase angle.
Z = √(30² + (40 − 80)²) = √(900 + 1600) = √2500 = 50 Ω.
tan φ = (40 − 80)/30 = −4/3 → φ ≈ −53° (current leads, capacitive).
Example 4 — Resonance: Find the resonant frequency for L = 2 H, C = 32 μF.
ω₀ = 1/√(LC) = 1/√(2 × 32 × 10⁻⁶) = 1/√(6.4 × 10⁻⁵) = 1/(8 × 10⁻³) = 125 rad/s (f₀ ≈ 19.9 Hz).
Example 5 — Transformer: A step-down transformer has 1000 primary and 100 secondary turns, with 220 V input. Find the output voltage.
Vs = Vp(Ns/Np) = 220 × (100/1000) = 22 V.
Important Question Patterns
1. RMS/peak (1–2 marks): convert between peak and RMS; why AC meters read RMS; why the average is zero.
2. Reactance & phase (2–3 marks): XL, XC and how they vary with frequency; phase relation for R, L, C.
3. Series LCR (3 marks): find Z, current and phase angle; identify inductive vs capacitive behaviour.
4. Resonance (3 marks): ω₀ = 1/√(LC); why Z is minimum and I maximum; application to radio tuning.
5. Power/transformer (3 marks): P = Vrms Irms cos φ, power factor, wattless current; transformer turns ratio and energy losses.
⚡ Quick Revision
- Irms = I₀/√2, Vrms = V₀/√2; meters read RMS; average over a cycle = 0.
- R: in phase. L: current lags 90°, XL = ωL. C: current leads 90°, XC = 1/ωC. ("ELI the ICE man.")
- Z = √(R² + (XL − XC)²), I = V/Z, tan φ = (XL − XC)/R.
- Resonance: XL = XC → ω₀ = 1/√(LC), Z minimum = R, I maximum, φ = 0 (radio tuning).
- P = Vrms Irms cos φ; power factor cos φ = R/Z; pure L or C → wattless current.
- Transformer: Vs/Vp = Ns/Np = Ip/Is; AC only; losses = copper, eddy, hysteresis, leakage.
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