Chapter 1 · Class 11-12 & JEE/NEET

Alternating Current

26 topics in 10 parts

Full lessonClass 12 Physics · EMI and Alternating Current Practice190 practice questions

Key formulas

RMS Current & Voltage
$I_{rms} = \frac{I_0}{\sqrt{2}} \approx 0.707\, I_0, \quad V_{rms} = \frac{V_0}{\sqrt{2}}$
Inductive & Capacitive Reactance
$X_L = \omega L = 2\pi f L, \quad X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$
Series LCR Impedance
$Z = \sqrt{R^2 + (X_L - X_C)^2}, \quad \tan\phi = \frac{X_L - X_C}{R}$
Resonance Frequency & Q-Factor
$f_r = \frac{1}{2\pi\sqrt{LC}}, \quad Q = \frac{\omega_r L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$

LCR series resonance Instantaneous AC Voltage & Current Phase Difference & Phase Angle Angular Frequency & Time Period Average Value of AC RMS Value of Current & Voltage

Key ideas

Phasor Representation and Phase Relationship in Series LCR

4. Systematic Comparison & Parameter Classifications

Component	Opposition (Reactance)	Phase Relation (V vs I)	Power Factor (cos φ)
Pure Resistor (R)	R (Resistance, Ohms)	In Phase (φ = 0°)	1.0 (Unity - Max Dissipation)
Pure Inductor (L)	X_L = ωL	Voltage LEADS Current by 90° (+π/2)	0 (Wattless Current)
Pure Capacitor (C)	X_C = 1/(ωC)	Voltage LAGS Current by 90° (-π/2)	0 (Wattless Current)
Series LCR Circuit	Z = √[R² + (X_L - X_C)²]	φ depends on (X_L - X_C)	cos φ = R / Z

Exam Worked Example

Problem: In a series LCR circuit, R = 30 Ω, X_L = 80 Ω, and X_C = 40 Ω connected to an AC source V = 100 sin(100πt) Volts. Calculate (a) Circuit Impedance Z, (b) Peak Current I_0, and (c) Power Factor cos φ.

● Step 1: Impedance Z = √[R² + (X_L - X_C)²] = √[30² + (80 - 40)²] = √[900 + 1600] = √2500 = 50 Ω.

● Step 2: Peak current I_0 = V_0 / Z = 100 / 50 = 2.0 Amperes.

● Step 3: Power Factor cos φ = R / Z = 30 / 50 = 0.60 (Lagging, since X_L > X_C).

Checkpoint

1. At electrical resonance in a series LCR AC circuit, what is the value of the power factor?

All 26 topics in Alternating Current

Phasor Diagrams
- Phase Difference & Phase Angle
- Phasor Representation
Average Value of Current
- Mean & Average Value
- AC Waveforms
RMS Value of Current
- Effective Current & Root Mean Square
- Peak Value & Peak Voltage
AC Circuits
- Circuit Containing Resistor Only
- Circuit Containing Inductor Only
- Circuit Containing Capacitor Only
- Capacitive Reactance
- Inductive Reactance
- RL Series Circuit
- RC Series Circuit
- Series LCR Circuit
Power in Series LCR Circuit
- Average Power Consumption
- Power Factor
- Wattless Component of Current
Resonance in Series LCR Circuit
- Resonant Frequency
- Q-Factor of Resonance
- Bandwidth & Half-Power Points
LC Oscillations
- Oscillation Frequency & Energy Conservation
- Damped LC Oscillations
Choke Coil
- Inductance & Power Loss
Transformers
- Turns Ratio & Voltage Transformation
- Efficiency & Power Losses
Skin Effect
- High Frequency Current Distribution