# ELEC1111 - Electrical Circuit Fundamentals

Last modified by Leon Luo on 2023/01/27 13:30

# Overview

The course is an introduction to Electrical Engineering to new aspiring Electrical Engineers or individuals who are interested in the basics of electrical systems. The course covers the basics of electrical elements and circuits and the technical skills needed to analyze these circuits. This includes topics such as fundamental electrical elements like sources, resistors, capacitors, inductors, and diodes, as well as DC and AC circuit analysis techniques like Kirchhoff's laws, nodal and mesh analysis, circuit theorems, and phasor representation. The course also covers DC and AC electrical circuits, including RC and RL circuits and operational amplifiers. Electrical engineering has a wide range of applications in many different industries. Some common applications of electrical engineering include:

1. Power generation, transmission, and distribution: Electrical engineers design and build systems for generating, transmitting, and distributing electricity, including power plants, transmission lines, and distribution networks.
2. Electronics: Electrical engineers design and develop electronic devices and systems, including computers, mobile phones, and other consumer electronics.
3. Transportation: Electrical engineers work on the design and development of electrical systems for transportation, including electric and hybrid vehicles, trains, and aircraft.
4. Communications: Electrical engineers design and build communication systems, including cell phone networks, satellite systems, and internet infrastructure.
5. Medical equipment: Electrical engineers design and develop medical equipment, such as CT scanners, MRI machines, and defibrillators.
6. Industrial control systems: Electrical engineers design and build control systems for factories and other industrial settings, including automation systems, process control systems, and robotics.
7. Renewable energy: Electrical engineers work on the design and development of renewable energy systems, such as solar panels, wind turbines, and hydroelectric power plants.

These are just a few examples of the many applications of electrical engineering. Electrical engineers are involved in the design and development of a wide range of products and systems that rely on electricity and electronics. By the end of the course, students should have a general understanding of what can be achieved with electrical engineering, be familiar with elementary concepts of electrical circuits and their analysis, and be familiar with basic laboratory equipment and techniques for measuring electrical quantities.

# Formula Summary

The course has its own math formula handbook on its moodle page. Similarly, ELSOC hosts a student formula sheet available to the public on their google drive.

## Notation

Constant variables are usually denoted with an uppercase character. I.e. constant charge is denoted as Q.

Instantaneous or varying variables are usually denoted as a function. I.e. time-varying charge is denoted as q(t). For convenience, the denotation is usually simplified to its function name. I.e. time-varying charge q(t) can be simplified to q.

## Physics Fundamentals

• Current:
$$i=\frac{d}{dt}q$$
• Charge:
$$q=\int_{t_0}^{t_1} i \, dt$$ where $$t_0 \leq t \leq t_1$$
• Voltage between two points:
$$v_a-v_b=v_{ab}=-v_{ba}=\frac{d}{dq}w$$

• Power:
$$p=\frac{d}{dt}w=vi$$
• Energy:
$$w=\int_{t_0}^{t_1} p \, dt=\int_{t_0}^{t_1} vi \, dt$$ where $$t_0 \leq t \leq t_1$$
• Conservation of Energy:
$$\sum p_{supplied} = \sum p_{absorbed}$$$$\sum p = 0$$

## Circuit Fundamentals

• Resistance:
$$r(t)=\frac{v(t)}{i(t)}$$
• Ohm's Law - Linear Resistance
$$R=\frac{V}{I}$$

# Concepts

These concepts are studied through course content, mainly lecture notes and course recommended textbooks. Please note, unless referenced from another source, please assume the following information presented is interpreted, studied, and re-expressed from the course content. Furthermore, please refer to the course content directly, e.g. ask the lecturer or read the textbook, for the most relevant knowledge required for the course.

## Fundamentals

Electrical Engineering stems from the various discoveries and efforts of scientists from the past.

### Physics Basis

Electrical engineering stems from the physics of electromagnetism. Further introduction of electromagnetism is covered in  PHYS1231 and the engineering application of electromagnetism in ELEC3115.

#### The Systems of Units

The System of Units refers to the International System of Units which is usually abbreviated as SI. The SI system

#### The Electric Charge

##### Current

Current by definition is the change in electric charge over the change in time.

$$i\triangleq\frac{dq}{dt}$$

Furthermore, the unit of current is amperes  $$\mathrm{A}$$ which is defined as 1 coulumb per 1 second for 1 ampere.
$$1\mathrm{A}=1\frac{\mathrm{C}}{\mathrm{s}}$$

Common notations for currents in electrical engineering
$$I$$ : Constant current
$$i(t)$$ : Instantaneous or time-dependent current. It should be further noted that  $$i(t)$$ can be simplified as $$i$$ . However, this simplification can lead to confusion with complex numbers which uses $$i$$ as the symbol for imaginary numbers. As a result, it is common to see the imaginary symbol, $$i$$ , be represented as $$j$$ in electrical engineering. In the context of ELEC1111 and ELEC2134, the use of $$j$$ is highly preferred over use of $$i$$ due to convention.

It is common in

## Nodal & Mesh Analysis

A circuit can be defined as a network of circuit elements that are interconnected such that there is a closed-path of electric flow between elements. The interconnection are usually wires between elements in a physical circuit.

## Operational Amplifiers

The operational amplifier, usually shortened to op-amp and its relevant variations, is an electronic voltage amplifier with a very high gain and a very high input impedence. As an amplifier, they are active elements. From the textbook, it can be thought of as an electronic module that behaves like a voltage-controlled voltage source. In the current evolution, the opamp is created from complex arrangments of transistors and relevant passive elements (i.e. resistors) and is usually provided as an integrated circuit product. Historically, the operational amplifier was originally developed using vacuum tubes. The operational part of the name in operational amplifiers hints its intended use. It is a general purpose device thats been designed to perform mathematical operations in analog circuits. The operations include addition, subtraction, multiplication, division, differentiation, and integration when appropriate circuit configurations is used with the opamp. Other than mathematical operations, their are other applications which includes voltage follower.

### Circuit Configurations

#### Non-inverting Amplifier

You are not allowed to create this diagram.

#### Voltage Follower

You are not allowed to create this diagram.

#### Summing Amplifier

You are not allowed to create this diagram.

#### Difference Amplifier

You are not allowed to create this diagram.

#### Integrator Amplifier

You are not allowed to create this diagram.

#### Differentiator Amplifier

You are not allowed to create this diagram.

# Recommended Resources

## Course Prescribed

### Textbook

• C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, 7th ed., New York, NY, USA: McGraw-Hill, 2021.

## Course Recommended

### Textbook

• R. C. Dorf and J. A. Svoboda, Introduction to Electric Circuits, 9th ed., Hoboken, NJ: John Wiley and Sons, 2013.
• J. D. Irwin and R. M. Nelms, Basic Engineering Circuit Analysis, 11th ed., Hoboken, NJ: John Wiley and Sons, 2015.

# Applications

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