FUNDAMENTALS OF KIRCHHOFF'S LAWS FOR ELECTRICAL ENGINEERS

Table of Contents

1. Introduction

2. Parts of an Electrical Circuit

3. Kirchhoff's Current Law

4. Kirchhoff's Voltage Law

1. Introduction

Kirchhoff's laws are basic analytical tools used to obtain solutions for currents and voltages in an electrical circuit. Circuits may be from a direct-current system or from an alternating current system. The following diagram depicts a simple resistive network.

Figure: Simple Resistive Network

Kirchhoff's laws of circuit analysis are reviewed in our FE Electrical exam review course. Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) are important for both DC and AC steady states, and they are important to understand for the FE exam.

2. Parts of an Electrical Circuit

(i) Node: In an electrical circuit, a node is the point where two or more components are connected. This point is usually marked with a dark circle or dot when being depicted on diagrams. The circuit in the diagram above includes nodes, which are labeled as "b" and "g." A point, or a node in a circuit, specifies a certain voltage level with respect to a reference point or node.

(ii) Branch: A branch is a traversing path between any two nodes in a circuit that have electrical elements. The above diagram shows that the circuit has seven branches, of which four are resistive branches (a-c, a-b, b-c, and b-g), and the other three branches contain voltage and current sources (a-b, a-g, and c-g).

(iii) Loop: A loop is any closed path in an electrical circuit. A loop in a circuit consists of branches that have a beginning point and an end point for tracing the path of electricity. In the above diagram, loops/closed paths include a-b-g-a and a-c-b-a. Further, it may be noted that the outside closed paths are a-c-g-a and a-b-c-g-a.

(iv) Mesh: A mesh is a special loop that does not include any other loops within it. The above diagram indicates that the three loops (a-b-g-a, b-c-g-b and a-c-b-a) are also considered meshes, while the loops a-c-g-a and a-b-c-g-a are not considered meshes.

3. Kirchhoff's Current Law:

KCL states that at any node in a circuit, the algebraic sum of currents entering and leaving a node at any instant of time must be equal to zero. Currents entering and currents exiting the node must be assigned opposite algebraic signs to assure the resultant equates to zero. Example: In the following figure, I1 - I2 + I3- I4 + I5 - I6 = 0. 

Figure: Kirchhoff's Current Law

4. Kirchhoff's Voltage Law

KVL states that in a closed circuit, the sum of all source voltages must be equal to the sum of all voltage drops. Voltage drops occur when the current flows from the higher potential terminal toward the lower potential terminal. Voltage rise occurs when current flows from a lower potential terminal toward the higher potential terminal or positive terminal of voltage source. 

Kirchhoff's Voltage Law from the figure: in clockwise direction starting from the voltage source is: V1 - IR1 - IR2- V2- IR3- IR4 + V3 - IR5 - V4 = 0, V1 - V2 + V3 - V4 = IR1 + IR2 + IR3 + IR4 + IR5

Figure: Kirchhoff's Voltage Law

Engineers preparing for the Fundamentals of Engineering Electrical and Computer exam should review Kirchhoff's laws prior to the exam in order to be able to estimate currents and voltages in an electrical circuit.

The Importance of Geology in Structural Engineering

Table of Contents

1. Introduction

2. Importance of Engineering Geology

3. The Need for an Understanding of Geology

1. Introduction

Geology is the study of the earth, its origin, structure, composition, and history. There are many forms of geology, including economic geology, planetary geology, and engineering geology. Engineering geology is a very important topic for structural engineers to understand as it helps them properly plan a project when considering the design, location, and other important geological factors.

2. Importance of Engineering Geology

Engineering geology helps ensure a safe and cost-effective design for construction projects. Gathering geological information for a project site is important in the planning, design, and construction phase of an engineering project. Conducting a detailed geological survey of an area before commencing a project will reduce the overall cost of the project. Common foundational problems in dams, bridges, and other buildings are typically directly related to the geology of the area where they were constructed. Our SE exam review course provides adequate geological information for engineers preparing for the SE exam.

3. The Need for an Understanding of Geology 

For quality control of construction materials, such as sand, gravel, or crushed rocks, an engineer with a geological background is needed. The knowledge of the nature of the rocks in a specific area is necessary for tunneling and determining the stability of cuts and slopes. Geological maps also help in planning projects. If geological features, such as faults, joints, beds, folds, or channels are encountered, suitable remedies should be incorporated. Geological maps provide information regarding the structural disposition of rock types in a proposed area. Topographical maps are essential for understanding the advantages and disadvantages of all possible sites. 

Hydrological maps provide information regarding the distribution of surface water channels and the occurrence and depth contour of ground water. Knowledge of ground water is necessary for excavation works. Understanding soil erosion transportation and deposition by surface water helps in soil conservation, river control, and coastal works. In geologically-sensitive areas, such as coastal belts and seismic zones, knowledge of the geological history of the area is very important. It is recommended that those preparing for one of the SE exams have a thorough understanding of geology and how to evaluate a site before a construction project.

Soil Erosion: Its Causes and Effects

Table of Contents

1. Introduction

2. Soil Erosion Factors

3. Agents of Soil Erosion

4. Soil Erosion by Water

5. Wind Erosion

6. Other Forms of Soil Erosion

1. Introduction

Soil is considered to be one of the most valuable natural resources. Soil is a combination of weathered rock, decayed organic matter, mineral fragments, water, and air. As degraded soil becomes loose and weak, it loses the ability to absorb and retain water, which leads to soil erosion. Ellison (1944) defines soil erosion as the process of detachment and transport of soil particles by erosive agents. 

2. Soil Erosion Factors

Factors that contribute to erosion include climate, topography, soil characteristics, vegetation, velocity of winds, rainfall intensity, and duration. Knowing the factors that cause erosion assists in identifying the source of erosion and developing a plan to control it. 

Erosion is classified into two major categories: geological erosion and man-made erosion. Geological erosion occurs naturally, while man-made erosion arises when humans alter the land. Soil classification and soil erosion factors are discussed in our FE Environmental exam review course to recap the fundamentals and factors of soil erosion.

3. Agents of Soil Erosion

4. Soil Erosion by Water

When a raindrop hits the soil, it destroys the granulation of soil (compaction) and causes a disruption of the soil surface (detachment). The exposed soil particles are dislodged, splashed into the air, and suspended in the rainwater. The rainwater that runs from a slope during heavy rains is referred to as a runoff. This runoff carries away soil particles and nutrient elements along with it.

There are three main types of erosion that occur due to water:

i) Sheet erosion is the uniform movement of a thin layer of soil from unprotected land.

ii) Rill erosion forms when the rainfall is heavy and runoff volume increases. Runoff rain water creates many small, deep channels called rills.

iii) Gully erosion evolves from rill erosion over time. When runoff is in a single wide and deep channel, it is known as gully erosion. A gully is defined as a scoured-out area that is not crossable with tillage and grading equipment.

Soil erosion by water is thoroughly discussed in our FE Environmental exam refresher course.

5. Wind Erosion

Wind erosion occurs when land that is bare of vegetation is exposed to high-velocity winds. Soil movement is initiated when the forces of wind are exerted against the surface of the ground. 

For each soil type and surface condition, there is a minimum velocity required to move soil particles; this concept is known as threshold velocity. When wind threshold velocity overcomes the cohesive and gravitational forces of the soil particles, wind can move soil and carry it away in suspension.

6. Other Forms of Soil Erosion

Gravity erosion is the transfer of rock and soil down a slope due to the direct action of gravity; gravity erosion can cause a mass movement of soil, ice, and rock, which leads to landslides, avalanches, and rock fall. 

Glacier erosion occurs when a huge mass of ice slowly moves over the land. Glaciers erode the earth's surface and wear down, pick up, and carry sediments that vary in size. 

Sedimentation control methods and the effects of soil erosion are important concepts to understand for the FE Environmental exam.

Wastewater Treatment Methods

Table of Contents

1. Introduction

2. Sources of Water Pollution

3. Wastewater Treatment

4. Methods of Wastewater Treatment

1. Introduction

Water is an ideal solvent with a neutral pH value and is colorless, odorless, and tasteless in its purest form. Any physical or chemical change in water that affects the health of a living organism is known as water pollution. Water can become contaminated due to domestic, industrial, physical, chemical, and biological pollutants. 

Water pollution is a global problem affecting millions of lives.

1. 1.8 billion people do not have access to clean water
2. 70% of all industrial waste is dumped into bodies of water
3. 2 million tons of sewage is disposed of into bodies of water each day throughout the world 
4. 840,000 people die each year from water-related diseases

2. Sources of Water Pollution

Water pollution comes in different forms and from different sources. 

1. Point-source pollution: pollutants derived from a single-known source (pipe or sewer line)
2. Nonpoint-source pollution: pollutants that come from many unknown sources (agricultural run-off)
3. Trans-boundary pollution: pollutants that affect the environment hundreds of miles away from the source (nuclear incident)

Water pollution and the causes of water pollution are thoroughly reviewed in our PE Environmental exam review courses.

3. Wastewater Treatment 

The water used for industrial and domestic purposes is degraded with pollutants, and such water must be treated to remove pollutants before being released into bodies of water. The aim of wastewater treatment is to remove suspended solids, salts, nutrients, bacteria, and oxygen-demanding material. Wastewater treatment is a large industry that is worth $20 billion a year. Therefore, it is important to study wastewater treatment methods prior to taking the PE exam. 

4. Methods of Wastewater Treatment

Wastewater is treated by using different methods to remove pollutants before returning the water to the drinking supply.

Two methods of water treatment are employed based on the need: 

1. Conventional method using sewage tanks
2. Centralized wastewater treatment plants

Wastewater treatment involves three stages: 

• Primary stage
• Secondary stage 
• Tertiary stage 

The three stages involved in wastewater treatment are explained in the following flow charts:

(i) Primary Treatment

Screening stage: Incoming raw sewage enters the treatment plant and passes through a series of screens to remove large, floating organic material.

Sedimentation stage: In the second stage, water enters the sedimentation tanks to remove sand, small stones, and grit. The particulate matter settles out to form a mud called sludge. In the next step, sludge is removed and transported to a digester. Primary treatment removes about 35% of biochemical oxygen demand (BOD) from the polluted water. 

(ii) Secondary Treatment

Secondary treatment is a biological process involving microorganisms. The wastewater is pumped into oxidation ponds where the microorganisms oxidize its organic matter, and then it is transferred from the primary sedimentation tank to the stabilization tank. The partly-treated water then enters the final sedimentation tank where the sludge settles. After the sludge is settled, it is transported to the digester.

(iii) Chlorination Stage

At this stage, the pH value of the water is near neutral. The BOD value of water is assessed, and the chlorination process is activated to kill harmful pathogens. After chlorination, water that is safe to use can be discharged. Secondary treatment removes about 90% of BOD. Secondary treatment does not remove all nutrients, heavy metals, solvents and pesticides. To be cautionary in regards to safety, water should be treated in an advanced stage that involves sophisticated methods and technology.

(iv) Tertiary Treatment

Tertiary treatment is a physicochemical process aimed to remove the turbidity of wastewater caused by nitrogen, phosphorus, dissolved organic matter, heavy metals, and pathogens. Tertiary treatment involves a chemical oxidation of wastewater using strong oxidizing agents, such as chlorine gas, perchlorate salts, ozone gas, and UV radiation. Tertiary treatment renders the water safe to be discharged back into the environment. 

Wastewater treatment topics are extensively discussed and emphasized in our PE exam review courses for both environmental engineers and water resources engineers.