1.1: Introduction

In this chapter we shall examine the major quantities of interest in electrical systems and describe their relationships. These include voltage, current, power, energy and resistance. We begin with basic definitions and proceed to example computations. We shall go beyond the theoretical and investigate practical aspects as found in electrical laboratories. This includes measurement devices and power sources, as well as various resistive devices. We shall examine batteries from a functional perspective, and perform computations regarding efficiency and cost of energy. We will also introduce some of the device symbols used to create electrical circuit schematics. This material presents the foundation upon which we will build circuit analysis techniques in subsequent chapters. Treat it accordingly.

Essential Math Skills Primer for Circuit Analysis

In the context of the introduction to circuit analysis, the following mathematical skills play a crucial role:

1. Algebra to Solve Systems of Equations:

   • Proficiency in algebra is essential for solving systems of linear equations, which commonly arise when analyzing electrical circuits. This skill is vital for determining unknown variables and understanding circuit behavior.

2. Calculus:

   • Calculus is employed to analyze rates of change and quantities such as voltage and current over time. Differential calculus aids in understanding instantaneous changes, while integral calculus is used for summation and accumulation in circuit analysis.

3. Ordinary Differential Equations (ODE):

   • ODEs are fundamental in modeling and understanding dynamic behavior in electrical circuits. They describe the relationships between variables and their rates of change, providing insights into circuit dynamics in the RC, RL, and RLC circuits.

4. Complex Number Operations:

   • Complex numbers are frequently encountered in circuit analysis, representing impedance, voltage, and current in AC circuits. Proficiency in complex number operations is crucial for handling impedance calculations and understanding circuit responses.

5. Coordinate Transformation:

   • Coordinate transformations are utilized to convert between different representations of circuit variables. Techniques like phasor analysis involve transforming time-domain signals into complex frequency-domain representations for easier analysis.

6. Laplace Transform:

   • Laplace transform is a powerful mathematical tool used to analyze linear time-invariant systems, common in circuit analysis. It simplifies the analysis of transient responses and facilitates solving differential equations in the frequency domain.