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Module Overview

In this module capacitors and inductors are introduced as circuit elements and then the natural and step response of first order circuits are studied. The module has been organized to first provide an introduction to inductors and capacitors as circuit elements. This section of the module can be omitted, if the student is already familiar with the material. The second part covers the natural and step response of simple RC and RL circuits. The results are then extended to general first order RC and RL circuits, by exploiting the student’s knowledge of Thévenin and Norton equivalent circuits an superposition.

Introduction
 
In this series of lectures capacitors and inductors are introduced as circuit elements and then the natural and step response of first order circuits are studied. The module has been organized to first provide an introduction to inductors and capacitors as circuit elements. This section can be omitted, if it is adequately covered elsewhere. The second part covers the natural and step response of simple resistor-capacitor (RC) and resistor-inductor (RL) circuits and extends the results to general first order RC and RL circuits, by exploiting the student’s knowledge of Thévenin and Norton equivalent circuits and superposition.
 
This module consists of a sequence of 26 videos with self-assessment questions keyed to specific videos. The videos provide an alternative to in-class lectures and reading the textbook. The videos can be assigned in place of regularly scheduled lectures or as additional material. It is expected that the course instructor, will supplement the module with additional questions and perhaps some problem solving tutorials and one or two laboratory exercises.
 
Prerequisites
 
Before starting this module, one should be familiar with;
  • circuit elements such as resistors, switches, voltage sources and current sources,
  • Kirchhoff’s Voltage and Current Laws, along with voltage and current division,
  • Thévenin and Norton equivalent networks and superposition
  • and finding the derivative and the integral of common functions, especially piecewise constant functions and the exponential function.

Learning Outcomes

With careful study, by the end of this module, one should be able to:
  • describe the behaviour of inductors and capacitors as circuit elements,
  • calculate the equivalent value of parallel and series combinations of inductors and
  • of capacitors.
  • analyze circuits containing inductors, resistors and capacitors driven by dc sources and determine the energy stored in the reactive elements,
  • evaluate the response of first order circuits to some initial stored energy,
  • and evaluate the response of first order circuits to step changes in their input voltage or current.

Explore Module

Please note that this preview is intended for exploration purposes only. If you'd like to use this interactive module in one of your courses,to ensure playback and tracking, you must upload the SCORM package (downloadable below) to your institution's Learning Management System (ex. Blackboard, D2L, Moodle, etc). 

PROJECT FILES
Type: Assessments
Title Author Description
Problems for First Order Step Response (Capacitors and Inductors) | Download File (70.58 KB) Dr. David G. Nairn
Type: Glossary
Title Author Description
Glossary | Download File (84.59 KB) Dr. David G. Nairn

This glossary contains definitions for the modules: Operational Amplifier (opamp) Circuits, First Order Step Response, and Sinusoidal Steady State Analysis.
Type: Instructor Guide
Title Author Description
The First Order Step Response - Facilitator Guide | Download File (12.27 KB) Dr. David G. Nairn

This document is designed to assist instructors who are interested in using this module as part of their course. It details what is included in the module as well as prerequisites and outcomes.
Type: Modules
Title Author Description
V1_2015_First Order Step Response (Storyline File) Dr. David G. Nairn

This Articulate Storyline File can be downloaded and modified to your specific learning objectives (within the bounds of the creative commons licensing selected for this file. This is encouraged, but any technical issues are not supported by the University of Toronto.
V1_2015_First Order Step Response (Storyline SCORM Package) Dr. David G. Nairn

This Articulate Storyline SCORM package can be uploaded into your institution's Learning Management System.
V2_2021_First Order Step Response (Rise SCORM Package) Prof. Belinda Wang

This Articulate Rise SCORM package can be uploaded into your institution's Learning Management System
Type: Video Links
Title Author Description
The Capacitor's Structure and Operation | The Capacitor's Structure and Operation Dr. David G. Nairn
Capacitors as Circuit Elements | Capacitors as Circuit Elements Dr. David G. Nairn
Example: Finding the Capacitor's Voltage | Example: Finding the Capacitor's Voltage Dr. David G. Nairn
Power and Energy Relationships | Power and Energy Relationships Dr. David G. Nairn
The Inductor's Structure and Operation | The Inductor's Structure and Operation Dr. David G. Nairn
Inductors as Circuit Elements | Inductors as Circuit Elements Dr. David G. Nairn
Power and Energy Relationships | Power and Energy Relationships Dr. David G. Nairn
Example: Energy Stored in Passive Elements | Example: Energy Stored in Passive Elements Dr. David G. Nairn
Capacitor and Inductor Combinations - Introduction | Capacitor and Inductor Combinations - Introduction Dr. David G. Nairn
Inductors in Series | Inductors in Series Dr. David G. Nairn
Capacitors in Series | Capacitors in Series Dr. David G. Nairn
Inductors in Parallel | Inductors in Parallel Dr. David G. Nairn
Capacitors in Parallel | Capacitors in Parallel Dr. David G. Nairn
Capacitor and Inductor Combinations - Summary | Capacitor and Inductor Combinations - Summary Dr. David G. Nairn
Example: Simplification of Circuit with Multiple Elements | Example: Simplification of Circuit with Multiple Elements Dr. David G. Nairn
Analysis of the RC Circuit's Natural Response | Analysis of the RC Circuit's Natural Response Dr. David G. Nairn
The Time Constant | The Time Constant Dr. David G. Nairn
Example: Natural Response of an RC Circuit | Example: Natural Response of an RC Circuit Dr. David G. Nairn
Analysis of an RC Circuit's Step Response | Analysis of an RC Circuit's Step Response Dr. David G. Nairn
Calculating the Step Response | Calculating the Step Response Dr. David G. Nairn
Example: Step Response of an RC Circuit | Example: Step Response of an RC Circuit Dr. David G. Nairn
Analysis of the RL Circuit's Natural Response | Analysis of the RL Circuit's Natural Response Dr. David G. Nairn
Analysis of an RL Circuit's Step Response (Part 1) | Analysis of an RL Circuit's Step Response (Part 1) Dr. David G. Nairn
Analysis of an RL Circuit's Step Response (Part 2) | Analysis of an RL Circuit's Step Response (Part 2) Dr. David G. Nairn
Natural and Step response of an RL Circuit - Summary | Natural and Step response of an RL Circuit - Summary Dr. David G. Nairn
Back to Parent Project
Electromagnetics and Circuits

This project is a set of 12 learning modules that support the teaching of foundational level electromagnetics and circuits in engineering programs. These modules could be used for an inverted or hybrid delivery of a first year course, or courses. We envision these modules partially or fully replacing in-person lectures, and being paired with in-person laboratories and other hands-on experiential learning activities to create an effective, active learning experience.

Project Lead(s): Prof. Belinda Wang
Project Collaborator(s): Dr. David G. NairnDr. Ajoy Opal
Project Team Members: Sean McAlary
Details
Used in:
ECE110

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