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EET - EM-7 VFP-2

DC Circuit Analysis (Kirchhoff’s Voltage Law) 1

VFP-2 – Lesson Preparation

o Topic : Kirchhoff's voltage laws

o Date and Time : Monday 20/ 10 / 2014 8:00 am

Mohammed Omar 104

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Table of Content

1. Didactic Reflection ..................................................................................................................................................... 3

1.1 Curriculum Analysis: ........................................................................................................................ 3

1.1.1 Module Description: .................................................................................................................................. 3

1.1.2 General objective of the module: ............................................................................................................ 4

1.1.3 Specific Objectives of module units: ...................................................................................................... 4

1.2 Content Analysis ............................................................................................................................. 5

1.2.1 First Kirchhoff's Voltage Law description ...................................................................................... 5

1.2.2 RCT Kirchhoff's Voltage Law description .............................................................................................. 8

1.2.3 The lesson Content description of Kirchhoff’s Voltage Law ............................................................ 10

1.3 Didactic Analysis ........................................................................................................................... 12

1.3.1 The environment ..................................................................................................................................... 12

1.3.2 Methods and Tools ................................................................................................................................. 13

2. Lesson Plan .............................................................................................................................................................. 15

2.1 Learning Objectives ....................................................................................................................... 15

2.2 Overview of the Intended Process ................................................................................................. 16

3. Bibliography ............................................................................................................................................................. 18

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1. Didactic Reflection

1.1 Curriculum Analysis:

The module name is Electrical Circuits-1 and its code is (ELT 106). The contact hours of

this module are 3 hours theory and tutorial per week without practical and its credit hours

are 3.

1.1.1 Module Description:

This module is taught in electrical department for first trimester and contains on six units:

Fundamentals of electrostatics

Batteries

Principles of DC circuits

DC circuits analysis

Electromagnetism

Magnetic circuits

In addition, explanation of electrostatics laws, batteries, DC circuit analysis,

electromagnetism and magnetic circuits. The course also include: capacitors, Ohm's law,

Kirchhoff's laws, series and parallel circuits, power, and DC bridges.

The topic of this lesson is Kirchhoff's voltage law and it is belonged to DC circuit analysis

unit. Before this units the trainees study two units are

Fundamentals of electrostatics

Batteries

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When they finished studying these two units they will come to DC circuit analysis unit.

under this unit there are five topics are:

Methods of DC circuit analysis.

Kirchhoff's current and voltage laws.

Mesh current method.

Node voltage method.

Superposition method.

1.1.2 General objective of the module:

The module is designed to give the trainees basic knowledge of electrostatic, batteries, and

fundamentals of DC current. Also covers DC circuits analysis, electromagnetism, and

magnetic circuits.

1.1.3 Specific Objectives of module units:

When the trainees finish each module units they will get some skills related to the unit so at

the end of trimester they have to be able to

Explain the basic electrostatics terms.

Describe the types of capacitors

Determine the total capacitance for different capacitor connections.

Describe the types of batteries and their constructions and connections.

Explain the different resistor connections and calculate the total resistance.

Explain and apply Ohm's law.

Represent Ohm's law graphically.

Apply Kickoff’s laws, and voltage and current division rules

Solve simple DC circuits.

Explain the principles of electromagnetism.

Solve simple magnetic circuits.

.

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1.2 Content Analysis

Kirchhoff's Voltage Law topic one of the most important topic in electrical department that

related to series circuits so there are different types of defining and explaining its steps in

the colleges..

1.2.1 First Kirchhoff's Voltage Law description

The following description of Kirchhoff's Voltage Law from firs research source is written by

Tony R. Kuphaldt under the Design Science License. (Kuphaldt, 2002)

This principle is known as Kirchhoff's Voltage Law (discovered in 1847 by Gustav R.

Kirchhoff, a German physicist), and it can be stated as such:

"The algebraic sum of all voltages in a loop must equal zero"

Let's take a look at our example series circuit, this time numbering the points in the circuit

for voltage reference:

Fig. 1.2.1

(Kuphaldt, 2002)

Series Circuit

If we connect a voltmeter between points 2 and 1, red test lead to point 2 and black test

lead to point 1, the meter would register +45 volts. Typically the "+" sign is not shown, but

rather implied, for positive readings in digital meter displays. However, for this lesson the

polarity of the voltage reading is very important and so I will show positive numbers

explicitly:

E2-1 = +45 V

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When a voltage is specified with a double subscript (the characters "2-1" in the notation

"E2-1"), it means the voltage at the first point (2) as measured in reference to the second

point (1). A voltage specified as "Ecd" would mean the voltage as indicated by a digital

meter with the red test lead on point "c" and the black test lead on point "d": the voltage at

"c" in reference to "d".

Fig. 1.2.2

(Kuphaldt, 2002)

voltmeter

If we were to take that same voltmeter and measure the voltage drop across each resistor,

stepping around the circuit in a clockwise direction with the red test lead of our meter on

the point ahead and the black test lead on the point behind, we would obtain the following

readings:

E3-2 = -10 V

E4-3 = -20 V

E1-4 = -15 V

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Fig. 1.2.3

(Kuphaldt, 2002)

voltages measurements

We should already be familiar with the general principle for series circuits stating that

individual voltage drops add up to the total applied voltage, but measuring voltage drops in

this manner and paying attention to the polarity (mathematical sign) of the readings reveals

another facet of this principle: that the voltages measured as such all add up to zero:

E2-1 = +45 V

E3-2 = -10 V

E4-3 = -20 V

÷ E1-4 = -15 V

0 V

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1.2.2 RCT Kirchhoff's Voltage Law description

The second explanation of Kirchhoff’s Voltage Law is written by Edvard Csanyfor

University of Liverpool. This content description is same RCT content. (Kirchhoff’s Laws,

2000)

The Kirchhoff’s Voltage Law, states that:

The algebraic sum of voltages around a closed circuit loop is zero.

There’s the phrase ‘algebraic sum’ again, so we must recognize that the direction of

voltages matters when using Kirchhoff’s Voltage Law.

Fig. 1.2.4

(Kirchhoff’s Laws, 2000)

circuit loop

Fig. 1.2.4 shows a circuit loop, which is part of a larger circuit. The loop involves four

nodes, ABCD, between which are connected four components. In this case the four

components are resistances, but Kirchhoff’s Voltage Law can be applied no matter what

components are connected in the closed circuit loop. The voltages across the four

resistances comprising the circuit loop have been defined as V1, V2, V3, V4 and

Kirchhoff’s Voltage Law allows us to write down an equation relating these voltages. If we

think about travelling around the closed circuit loop in any direction, we note that the four

voltages will be encountered in sequence.

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Two of the voltage arrows will point in the direction of travel and two will oppose the

travel. The algebraic sum of voltages needs to take account of this difference in relative

direction.

To apply Kirchhoff’s Voltage Law correctly, we must make arbitrary choices about the

direction of travel around the closed circuit loop and the contribution which the separate

voltages make to the algebraic sum around the closed circuit loop. Suppose we travel

around the loop in the clockwise direction (ABCD) and that voltages opposite to the

direction of travel make a positive contribution to the algebraic sum. In travelling from A to

B the voltage V1 is encountered and it is in a direction which is opposite to the travel.

sum. Expressed mathematically, the algebraic sum of voltages around the closed loop

ABCD is: + V1 + V2 – V3 – V4 and Kirchhoff’s Voltage Law states that this sum is equal to

zero:

+ V1 + V2 – V3 – V4 = 0 (2.4)

The other two combinations are:

Clockwise around the loop (ABCD), with the arrow positive:

- V1 – V2 + V3 + V4 = 0 (2.5)

Anticlockwise around the loop (ADCB), against the arrow positive:

- V1 – V2 + V3 + V4 = 0 (2.6)

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If we go through these two these descriptions we will not see much different but there are two

main different

Table 1.2.1

First Content Description Second Content Description (RCT)

The direction of resistor voltage is same with

its current which is flow through it.

The direction of resistor voltage is opposite

with its current which is flow through it.

.The source current goes from minus to

positive.

The source current goes from positive to

minus.

The topic is explained with practical way. The topic is explained only theoretical.

Contents Comparison

1.2.3 The lesson Content description of Kirchhoff’s Voltage Law

Kirchhoff's Voltage Law (KVL) states that the algebraic sum of the voltages across any set

of branches in a closed loop is zero.

∑Voltages across branches = 0

Below is a single loop circuit. The KVL computation is expressed graphically in that

voltages around a loop are summed up by traversing (figuratively walking around) the loop.

Before we start applying KVL we have to draw

current directions and voltages polarity for each

element. The direction of the current goes from

positive to negative side and the polarity of the

resistors is shown in the figure. The KVL

equation is obtained by traversing a circuit loop in

either direction and writing down unchanged

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the voltage of each element whose “+” terminal is entered first and writing down the

negative of every element’s voltage where the minus sign is first met. The loop must start

and end at the same point. It does not matter where you start on the loop.

Now we can apply KVL if we start from point 1 we have to finish at the same point :

9 V - 1.5 V - 5 V - 2.5 V = 0

Note that a current direction must have been assumed. The assumed current creates a

voltage across each resistor and fixes the position of the “+” and “-” signs so that the

passive sign convention is obeyed. The assumed current direction and polarity of the

voltage across each resistor must be in agreement with the passive sign convention for

KVL analysis to work.

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1.3 Didactic Analysis

Kirchhoff's voltage law very important lesson for Electrical Department trainees because

they will use it in the next lesson to analysis DC circuits and also in the next trimesters..In

the lesson will be two different way of teaching theory and practical to help the trainees to

understand the lesson very well and to apply the lesson steps in small experiment.

1.3.1 The environment

In this class there are 17 trainees and the rate ages of this class is 18 - 22 years old. All

trainees in this class are belonged to electrical power specialization. They got their

certificates from high schools so they are in the same level. As we observed during our

visits to this class me and my colleagues the trainees help each other ( good cooperation)

and good interacting with a trainer.

The lesson will be at Riyadh College of Technology in the second floor of Electrical

Department number 19 in class F28. The classroom is not well equipped so it need

ordering and organization. The classroom holds some materials such as tables, chairs,

projector and two whiteboards one for projector showing and the other for writing.

In RCT the study language is Arabic the system there is trimester. The will start at 8.00am

this time is very good for students because it is the first lesion and the will be fresh.

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1.3.2 Methods and Tools

This topic (Kirchhoff's voltage law) is new for trainees and related to the lessons before so

during the lesson will used different methods are

Lecture

Classroom Conversation

Group Work

Discovery (Experiment)

Individual Work

To perform this lesson in good condition should bring

PowerPoint presentation

Whiteboard and board markers to explain examples and draw the circuits.

Worksheets for group work and individual tasks.

Electrical board, wires and resistors to do the experiment.

Electrical Measuring Device (voltmeters)

Also the trainees should bring their materials are

Handbook

Calculator

Notebook

To hold the trainees attention the beginning of the lesson shall be with deductive approach

by making small review asking some questions about last two lessons. After that Lecture to

explain Kirchhoff's voltage laws definition and how to draw the directions of current and

voltages and we work with different series circuits.

Classroom Conversation to solve examples about Kirchhoff's voltage law and see different

answers and correct them by students.

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Group work to let the trainees do some work and discussion between each other.

Experiment as is known the content at RCT theory this will be new method for trainees so

the practical step will make the trainees interesting to understand the lesson.

Individual work will gives the trainer chance to assess the trainees and his work at the end

of the lesson.

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2. Lesson Plan

2.1 Learning Objectives

General Learning Objectives:

The Trainees …

1) connect the resistors in series connection (Cognitive ).

2) Measure the current and voltage in electrical circuits (psychomotor/ Cognitive).

Specific Learning Objectives:

The Trainees …

3) define Kickoff’s Kirchhoff's voltage law(Cognitive/Reorganization).

4) Apply Kickoff’s Kirchhoff's voltage laws on series circuits with different type circuits

(Cognitive/Reorganization).

5) solve simple DC circuits calculating the total current and the voltages across each element

(Cognitive/Transfer).

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2.2 Overview of the Intended Process

Opening / Entrance / Motivation

Methodology Media

Time

Minutes Expected Trainer-action Expected Trainee-action

Asking the trainees about

Ohm's law and electrical

power law and write it on the

whiteboard .

interact with the trainer and

write the triangles of electrical

power and Ohm's law.

deductive

Approach

Classroom

Conversation

Whiteboard

3

Body (Information / Elaboration)

Methodology Media

Time


Definition and explanation

of Kirchhoff's voltage law

by drawing series circuit

and demonstration how

Kirchhoff's voltage law

works.

Lecture

Projector

slide

1 , 2

5

Presents the series circuit

with three resistors and one

battery after that asks the

trainees to apply Kirchhoff's

voltage law.

Tracking the circuit and apply

Kirchhoff's voltage law steps.

Classroom

Conversation

Projector

slide

3

Whiteboard

4

Gives an example with

three resistors and three

unknown voltages to solve

it with the trainees.

Determining the unknown

voltages by using Kirchhoff's

voltage law.

Classroom

Conversation

Projector

slide

4

Whiteboard

6

Divides the class into three

groups and distribute the

work sheet of group work.

sharing in groups to solve the

tasks. Finding the voltage,

current and electrical power by

using different laws that they

have learned before. .

Group Work

Classroom

Conversation

Projector

slide

5

Whiteboard

10

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Asking the trainees to

solve and explain the tasks

on whiteboard.

One trainee from each group

solves and explains one

passage.

Classroom

Conversation

Worksheet

( 1 )

Gives the trainees change

to check how Kirchhoff's

voltage law works in

practical ways

connecting the resistors in

series and measure the

voltages and current according

to Kirchhoff's voltage law .

Discovery

Experiment

Projector

slide

6

Electrical

boards

Worksheet

( 2 )

12

Close (Reflection, Exercises, Homework, Feedback)

Methodology Media

Time


Distributes the work sheet of

quiz and asks the trainees to

solve it individually.

The trainees determine the

voltages by Kirchhoff's voltage

law and electrical power.

Individual

work

Projector

slide

12

Worksheet

( 3 )

10

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3. Bibliography Kirchhoff’s Laws. (2000, 1 3). Retrieved 10 14, 2014, from Electrical Engineering Portal: http://electrical-

engineering-portal.com/resources/knowledge/theorems-and-laws/kirchhoffs-laws

Kuphaldt, T. R. (2002, 6 5). Kirchhoff's Voltage Law (KVL). Retrieved 10 16, 2014, from All about circuits:

http://www.allaboutcircuits.com/vol_1/chpt_6/2.html

vfp 2 -1-

Design

module description

content analysis

didactic analysis

curriculum analysis

kirchhoffs voltage laws

eet em

electrical circuits

didactic reflection