Alternating Current — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Alternating Current (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Alternating Current (CBSE & HBSE)
CBSE emphasizes phasor diagrams, series LCR resonance derivation, power factor, and transformer efficiency calculations. HBSE focuses on RMS and peak values, reactance definitions, resonance condition, and basic AC circuit numericals.
AC Fundamentals: RMS, Peak Values, Phase
Alternating Current (AC)
AC is current that periodically reverses direction. Most common form is sinusoidal:
i = I₀ sinωt v = V₀ sinωt
where:
- I₀, V₀ = peak (maximum) values
- ω = angular frequency = 2πf = 2π/T
- f = frequency (Hz); T = time period (s)
RMS (Root Mean Square) Values
RMS value is the equivalent DC value that produces the same heating effect:
I_rms = I₀/√2 ≈ 0.707 I₀ V_rms = V₀/√2 ≈ 0.707 V₀
India: V_rms = 220V, f = 50Hz → V₀ = 220√2 ≈ 311V
Average Value
I_avg = 2I₀/π ≈ 0.637 I₀ (over half cycle)
Over complete cycle, average of AC = 0.
Phase in AC Circuits
Phase describes the temporal relationship between voltage and current:
| Element | Phase relationship | Phasor |
|---|---|---|
| Resistor R | V and I in phase (φ=0) | V∥I |
| Inductor L | V leads I by 90° (φ=+π/2) | V⊥I (V ahead) |
| Capacitor C | V lags I by 90° (φ=−π/2) | V⊥I (I ahead) |
Phasor Representation
A phasor is a rotating vector that represents the amplitude and phase of an AC quantity.
- Phasor length = amplitude (peak value)
- Phasor angle = phase angle with reference
- V and I can be added as vectors for AC circuits
Power Factor
cos φ = ratio of resistive component to total impedance
P = V_rms × I_rms × cos φ
- For pure R: cos φ = 1; P = V_rms × I_rms (maximum)
- For pure L or C: cos φ = 0; P = 0 (no power consumed!)
Diagram Indicator: [Sinusoidal AC waveform showing V₀, I₀, V_rms, I_rms; also phasor diagram showing V leading I by 90° for inductor.]
AC Circuits: R, L, C and Series LCR
Pure Resistive Circuit
- V = V₀ sinωt; I = (V₀/R) sinωt
- In phase (φ = 0)
- Power: P = V_rms I_rms = V²_rms/R
- Impedance: Z = R
Pure Inductive Circuit
- V = V₀ sinωt; I = (V₀/X_L) sin(ωt − π/2)
- Current lags voltage by 90°
- Inductive Reactance: X_L = ωL = 2πfL (Ω)
- X_L increases with frequency
- Power: P = 0 (no energy dissipated, stored in L)
Pure Capacitive Circuit
- V = V₀ sinωt; I = (V₀/X_C) sin(ωt + π/2)
- Current leads voltage by 90°
- Capacitive Reactance: X_C = 1/(ωC) = 1/(2πfC) (Ω)
- X_C decreases with frequency
- Power: P = 0 (no energy dissipated, stored in C)
Series LCR Circuit
Circuit containing L, C, R in series with AC source:
Impedance: Z = √(R² + (X_L − X_C)²)
Phase angle: tan φ = (X_L − X_C)/R
Current: I = V/Z = V₀/(Z) sin(ωt − φ)
Phasor Analysis of LCR Circuit
- V_R is in phase with I
- V_L leads I by 90°
- V_C lags I by 90°
- V = √(V_R² + (V_L − V_C)²)
Cases
| Condition | X_L vs X_C | φ | Nature |
|---|---|---|---|
| X_L > X_C | Inductive dominant | φ > 0 | V leads I |
| X_L < X_C | Capacitive dominant | φ < 0 | I leads V |
| X_L = X_C | Resonance | φ = 0 | V and I in phase |
Frequency Response
- Low frequency: X_C >> X_L → capacitive
- High frequency: X_L >> X_C → inductive
- Resonant frequency: X_L = X_C, Z minimum
Diagram Indicator: [Series LCR phasor diagram showing V_R along I, V_L perpendicular (leading), V_C perpendicular (lagging), resultant V at angle φ to I; also impedance triangle with R, (X_L-X_C), Z.]
Resonance, Power Factor and Transformers
Resonance in Series LCR
At resonance frequency ω₀: X_L = X_C → ωL = 1/(ωC)
ω₀ = 1/√(LC)
f₀ = 1/(2π√(LC))
At resonance:
- Z = Z_min = R
- I = I_max = V/R
- φ = 0 (V and I in phase)
- cos φ = 1 (maximum power factor)
Quality Factor (Q-factor)
Measure of sharpness of resonance:
Q = ω₀L/R = 1/(ω₀CR) = (1/R)√(L/C)
- High Q → sharp resonance, narrow bandwidth, selective circuit
- Q = resonant frequency/bandwidth = f₀/Δf
Bandwidth
Δf = f₀/Q = R/(2πL)
Frequency range where I ≥ I_max/√2 (power ≥ half max power = −3dB points).
Power in AC Circuits
P = V_rms I_rms cos φ = I²_rms R
cos φ = R/Z = power factor
| Circuit | Power factor | Average power |
|---|---|---|
| Pure R | cos φ = 1 | P = V_rms I_rms |
| Pure L | cos φ = 0 | P = 0 |
| Pure C | cos φ = 0 | P = 0 |
| LCR at resonance | cos φ = 1 | P = V_rms I_rms |
| LCR off resonance | 0 < cos φ < 1 | P = V_rms I_rms cos φ |
Wattless current: Component of I that contributes zero power (I sinφ)
Transformer
Based on mutual induction between primary and secondary coils.
Ideal transformer relations: V_s/V_p = N_s/N_p = I_p/I_s
Efficiency: η = (P_out/P_in) × 100% = (V_s I_s)/(V_p I_p) × 100%
Energy losses in transformers:
- Copper losses (I²R in windings)
- Eddy current losses (reduced by lamination)
- Hysteresis losses (reduced by soft iron core)
- Flux leakage
Applications
- Radio tuning: Series LCR resonance selects specific frequency
- Power transmission: Step-up transformer for long-distance (reduces I, reduces I²R loss)
- Home use: Step-down transformer (11kV → 220V)
Diagram Indicator: [Graph of I vs frequency for series LCR showing resonance peak at ω₀=1/√LC; bandwidth Δω marked; Q factor shown as height/width ratio. Also transformer diagram with primary/secondary labeled.]
Frequently asked questions
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Yes. The Alternating Current notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Alternating Current chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Alternating Current.