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7. ALTERNATING CURRENT

The chapter covers alternating current (ac) and its properties, particularly focusing on ac voltages and currents as they apply to resistors, inductors, and capacitors. Key topics include the phase relationships between voltage and current, the use of phasors for circuit analysis, resonant frequency in RLC circuits, and the function of transformers in altering voltage levels. The chapter concludes with various exercises and practical applications of these concepts.

Sections

ALTERNATING CURRENT

Alternating current (AC) is characterized by a voltage that varies over time, commonly representing electrical energy distribution, with key properties that differentiate it from direct current (DC).

7 Section Overview

Start current section content and materials

7.1 INTRODUCTION

This section introduces alternating current (AC) and its significance compared to direct current (DC), highlighting its widespread usage in electrical systems.

7.2 AC Voltage Applied to a Resistor

This section discusses how alternating current (AC) voltage applied to a resistor behaves, demonstrating key concepts such as phase relationship, current amplitude, and power dissipation.

7.3 AC VOLTAGE REPRESENTATION OF CURRENT AND VOLTAGE BY ROTATING VECTORS (PHASORS)

This section introduces the concept of phasors, which are used to represent ac voltages and currents, showing the phase relationships between them.

7.4 AC VOLTAGE APPLIED TO AN INDUCTOR

This section explores how an alternating current (AC) voltage affects an inductor, emphasizing the concepts of inductive reactance and the phase difference between current and voltage.

7.5 AC VOLTAGE APPLIED TO A CAPACITOR

This section discusses how alternating current (AC) interacts with capacitors, explaining the concepts of current and voltage in capacitive circuits.

7.6 AC Voltage Applied to a Series LCR Circuit

This section discusses the behavior and analysis of an LCR circuit connected to an AC voltage source, highlighting the phase relationships and powers involved.

7.6.1 Phasor-diagram solution

This section explains the use of phasors in analyzing the current and voltage relationships in AC circuits, particularly within a series RLC circuit.

7.6.2 Resonance

Resonance in series RLC circuits occurs when the resonant frequency matches the natural frequency of the system, leading to maximum current amplitude.

7.7 POWER IN A CIRCUIT: THE POWER FACTOR

This section explores the concept of power factor in AC circuits, detailing how it influences power consumption and the relationships between voltage, current, and phase angle.

7.8 TRANSFORMERS

Transformers are devices that change alternating voltages through the principle of mutual induction.

7.9 Summary

This section summarizes key concepts related to alternating current (AC) circuits, including voltage, current relationships, reactance, power, and transformers.

Learning Objectives

  • Alternating currents exhibit sinusoidal voltage variations over time.

  • The current through a resistor is in phase with the applied voltage, while it's not the case for inductors and capacitors.

  • Resonance in RLC circuits occurs at a specific frequency where inductive and capacitive reactances cancel each other.

Key Concepts

RMS voltage (V)

The effective voltage value for alternating current, given by V = 0.707 * V_m, where V_m is the peak voltage.

Inductive reactance (X_L)

A measure of the opposition that an inductor offers to AC, defined as X_L = ωL.

Capacitive reactance (X_C)

The opposition that a capacitor offers to AC, defined as X_C = 1/ωC.

Power factor

The ratio of the real power flowing to the load to the apparent power in the circuit, defined as cos(φ), where φ is the phase difference between current and voltage.

Transformer

A device that changes the voltage level of alternating current through electromagnetic induction between coils.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting