AC Circuit Analysis Lecture

Introduction

• Last class: Complex phasor representation from trigonometrical functions.
• Current topic: AC circuit analysis.
• Focus: Components in AC circuits, their behavior, quantification, and use in phasor calculations.

Key Components in AC Circuits

• Resistance:
  • Previously covered in DC context.
• Inductance & Capacitors:
  • Introduced for AC context.

Impedance in AC Circuits

• Ohm's Law for AC: V = IZ, where Z is impedance.
• Impedance (Z): Phasor voltage/phaser current ratio, measured in ohms.
• Types of loads in AC:
  • Resistors
  • Inductors
  • Capacitors
  • Phase shifts in currents are due to these components.

Resistance

• AC resistance: Peak voltage divided by peak current.
• Voltage and current in phase for resistors in AC.

Capacitors

• Passive element, stores energy in an electric field.
• Characteristics:
  • Voltage across cannot change instantaneously.
  • Acts as an open circuit for DC.
• Capacitance: Ability to store charge, depends on permittivity, distance, and area.
• Capacitive reactance: 1/(ωC) (Negative imaginary value in phasor).
• Current leads the voltage by 90 degrees.

Inductors

• Passive element, stores energy in a magnetic field.
• Characteristics:
  • Current through cannot change instantaneously.
  • Acts as a short circuit for DC.
• Inductive reactance: ωL (Positive imaginary value in phasor).
• Current lags voltage by 90 degrees.

AC Circuit Analysis

• Impedance (Z):
  • AC version of resistance, complex number with real and reactive parts.
• Analysis using phasors simplifies complex number arithmetic.

Series and Parallel Impedances

• Series:
  • Sum of impedances.
• Parallel:
  • Reciprocal sum of impedances.
  • Special case: Equal impedances.

Example Problems

• Example 1: Series circuit with resistor, inductor, and capacitor.
  • Current calculation shows lagging due to inductive reactance.
• Example 2: Parallel circuit with inductor and capacitor.
  • Use of voltage divider theorem.

Conclusion and Summary

• Summary of AC circuit behavior.
  • Resistive loads: Current in phase with voltage.
  • Inductive loads: Current lags voltage.
  • Capacitive loads: Current leads voltage.
• Practicality of remembering component behaviors and using anagram "CIVIL" for phase relations.

• The lecture covers practical applications, derivations, and example problems to enhance understanding of the discussed topics.