Introduction

The Engineering Sciences topic covers 6 to 9 questions on work, energy, power, heat, charge, forces, capacitance and inductance. These are all the topics that lead up to the Electromagnetics topic in Section 12. It also elaborates the previous section Properties of Electrical Materials from the materials perspective to the actual device behavior. For example, Properties of Electrical materials focused on the materials used to make an inductor and the properties of those materials. This topic shows how material characteristics are used to calculate the voltage difference and the energy across an inductor.

2.0 WORK, ENERGY, POWER & HEAT

These topics are very broad, but when applied to electrical engineering, they become focused on the work and energy that results from the electrical and magnetic forces as well as the power and heat produced by motors and generators. The latter is where these topics begin to overlap with mechanical engineering. The following descriptions focus on the broader definition of work, energy and power. Work, energy, and power are discussed again later in this section, but in how it relates to circuits and charge.

Energy is the capacity to do work. It comes in many forms: thermal, electrical, mechanical, chemical, electromagnetic, etc. Energy is given in units of joules, watt-hours (electrical energy), ft-lb, or Btu (heat). The two major types of energy used in electrical engineering are potential and kinetic energy.

Potential energy is the energy that is stored. In the physical world, that means the energy stored in an object due to its height, like when a ball ready to drop, or the energy stored in a compressed spring. In electrical engineering there is potential energy in a battery. See the next topic, 3.0 Charge, Energy, Current, Voltage & Power, for energy calculations related to batteries, capacitors, and inductors.

Kinetic Energy (KE) is the energy of a particle due to motion. Imagine a moving car. Since you know it will take an enormous amount of energy to stop it, it must mean there is energy in its movement. The heavier it is or the faster the car is moving, the more energy it has.

In electrical engineering we are interested in the kinetic energy from moving electrical charges. The equation above can be used to calculate the energy from a moving charge with mass, m.

The law of conservation of energy states that energy in a closed system with no external forces remains constant. Thus the sum of the total energy at time t =1 must equal the total energy at time t = 2. This is an important concept to understand. Essentially the energy must go somewhere. Potential energy can be converted to kinetic energy, i.e. a ball drops: the potential energy turns into kinetic energy of the falling ball.

You also need to understand the difference between work and energy. Work is the amount of energy used to move an object and is defined as the product of a force vector and the caused displacement. The work of a force acting upon a displacement is shown as the equation below.

Work has the same units as energy, so it can also be added to the conservation of energy equations to produce the work-energy principle. The principle states that the work done on an object is transferred to kinetic energy and vice versa.

The basic concept is that energy is conserved or transferred to work. You can use these conservation equations to solve for unknowns. You should use Work-Energy equations for when the length of time is not a factor.

Power is a rate of energy or work. In electrical engineering application, a generator produces electrical power or a motor requires electrical power.

Power is commonly given in units of watts (electrical), horsepower (mechanical), or btu/h (heat). The more power you have, the more work you can do in a given amount of time. For example, someone with a lot of muscles (power) can lift much heavier boxes (i.e. do more work) than someone with less.

The amount of power that is used over time is calculated as the energy consumed. In order to produce the power to do the heavy lifting in the previous example, energy was consumed via food. Power can also be stored over time as energy in a battery.

Heat is a form of energy, i.e. thermal energy. Typically heat is produced by resistance or friction. Since the law of conservation of energy says that energy can’t be created or destroyed, the inefficiencies in a system show up as heat. For example, when electricity is sent to a light bulb, electrical energy is converted to light energy or electromagnetic energy. Then, the energy that was not used to produce light is wasted as heat or thermal energy. This is why incandescent light bulbs, which get hot, are less efficient than CFL or LED light bulbs; energy is wasted as heat. This is different from power factor losses, which will be explained later.

This section is continued in the technical study guide, also there are many more practice exam problems.

3.0 CHARGE, ENERGY, CURRENT, VOLTAGE & POWER

An electric charge, Q, describes the number of electrons or protons there are. It can be positive (protons) or negative (electrons) and is measured in Coulombs (C). For example, one electron has -1.6 x 10-19 C of charge and one proton has +1.6 x 10-19 C. The movement of electrons is the foundation of how electricity works. It is unlikely that charge itself will be tested. It is more important to understand how charge is used to describe other concepts like current, power, voltage, and energy.

Current, I, is the movement of charge and is more specifically defined as the rate at which charge flows. It is represented in terms of Amps, where one amp is equal to the movement of one Coulomb of charge per second.

For steady flow, current can be calculated as:

One characteristic to distinguish is that current flows in the opposite direction of electrons. Current flows from positive to negative, see the green arrow in the figure below, start at the positive end of the battery, loop around the circuit and end at the negative end. Electrons on the other hand are attracted to positive charge, so it will flow from negative to positive, as shown in red below.

Figure 1: Current flows in a circuit from the positive end of the battery to the negative, as shown in green, while electrons flow from negative to positive.

Direct current (DC) is the supply of current in one direction. As mentioned previously, current flows from the positive voltage terminal to the negative terminal in a circuit. Current is deemed positive when it flows in this direction. Current is considered negative when it flows from a negative terminal to a positive terminal. DC current is a constant source and does not switch between negative and positive. The simplest example of a DC source is a battery.

Alternating current (AC) is able to supply current in both directions, positive to negative and negative to positive. This is shown in the graph below, where the current can be positive (above the 0-axis) or negative (below the 0-axis). Alternating current is what is supplied by the electric company to buildings. Alternating current is further discussed in the Alternating Circuits topic.

Figure 2: In an AC circuit, current can alternate its flow from positive to negative. In a DC circuit, current is constant.

Voltage, V is the potential energy in electricity; it is the amount of energy held in one charge and is given in units of volts.

Figure 3: A basic DC circuit, current flows from positive to negative.

Voltage is measured between two points because potential energy is the difference in energy. This potential energy in a circuit is what drives the flow of electrons, and therefore the current, from one point to the next. A battery is typically a source voltage, supplying energy into a circuit. A voltage can also be measured across a load or a resistor, this is known as voltage drop since the energy is being absorbed by the load.

This section is continued in the technical study guide, also there are many more practice exam problems.

4.0 FORCES BETWEEN CHARGES

Force is the action that pushes or pulls an object. The force can be invisible like gravity, electrical or magnetic.

One of the first set of concepts that you should know are Newton’s Three Laws of Motion. The application of these laws is tested very briefly on the electrical exam, since the focus for forces is primarily on electrical and magnetic forces. However, as a recap, here are the three laws below.

First Law: The first law states that an object at rest or at constant velocity (zero acceleration) will remain that way, until an unbalanced force acts upon the object.

Second Law: The second law states that an object subject to an unbalanced force will be subject to an acceleration that is directly proportional to the unbalanced force and inversely proportional to the object’s mass.

Third Law: The third law states that objects that are in contact with each other will experience a force opposite the subject force acting upon the object. This force is called the reaction force. This law is useful in the beam type problems.

The units of force may be given in US customary system (USCS) or the International System (SI) units for the FE exam. This means that force is measured in pounds (lbf) for USCS. Mass is given in terms of slugs ((lbf*s^2)/ft) or in pound-mass (lbm). See the Fluid Mechanics section for discussions on pound-force and pound-mass. For SI units, force is measured in Newtons ((kg*m)/s^2 ) and mass is given in terms of kilograms (kg). Make sure you know where to find the conversions between the two sets of units in your NCEES FE Reference Handbook.

There are two main forces that you should know for the Electrical FE exam, the electrical force and the magnetic force. These forces are covered in more detail in Section 12.0 Electromagnetics with the Maxwell Equations and Electrostatics/Magnetostatics, but this section will give you an introduction to these two forces.

First, an electrical force is the force produced between electric point charges. Based on Coulomb’s Law, opposite charges attract and like charges repel. The magnitude of the force between two point charges can be calculated based on the relationship below, as found in the NCEES FE Reference Handbook.

The unit vector a_12 will point away from charge 1 if they are like charges and towards charge 1 if the charges are opposite.

When looking at two charges the force vector will be in line with the charges, and will be equal in magnitude and opposite direction from charge 1 to 2 and from charge 2 to 1: F_12 = -F_21.

Figure 4: Like charges (negative) repel. Forces will be directed away from each other.

Figure 5: Like charges (positive) repel. Forces will be directed away from each other.

Figure 6: Opposite charges (positive and negative) attract.

The NCEES FE Reference Handbook shows equations that calculate the force on a change due to an electric field. An electric field, E, is a vector field of electric forces produced around a charged object. As derived from the equation below, each vector is a force per unit charge.

For a point charge, the electric field at position x_1 due to the source charge Q_S can be simplified by combining the previous two force equations.

The equation for the electric field at position x_1 is simplified as follows.

This can be thought of as a force at location x_1 that arises when there is a charge of magnitude +1C at x_1, in other words the force per unit charge at x_1. Now imagine finding the forces at various positions, x_i with the unit charge +1C. This would produce the field of forces per unit charge, i.e. the electric field.

Figure 7(a): An electric field from a positive point charge directs away from the charge. (b): An electric field from a negative point charge is directed toward the charge.

Figure 8: Electric fields between point charges (a): Opposite charges attract. (b): Like charges repel.

This section is continued in the technical study guide, also there are many more practice exam problems.

5.0 WORK, MOVING CHARGE IN ELECTRIC FIELD, VOLTAGE RELATIONSHIP WITH WORK

This section is continued in the technical study guide, also there are many more practice exam problems.

6.0 CAPACITANCE

This section is continued in the technical study guide, also there are many more practice exam problems.

7.0 INDUCTANCE

This section is continued in the technical study guide, also there are many more practice exam problems.

8.0 Practice Problems

8.1 PRACTICE PROBLEM 1 – ELECTRIC FORCE

8.2 PRACTICE PROBLEM 2 – ELECTRIC FIELD

8.3 PRACTICE PROBLEM 3 - CAPACITANCE

Practice Problems 4 through 9 and all solutions included in the technical study guide, along with many more practice exam problems.