Chapter 3 Bartha‟s model and its trial application to the “top-down” analogy
3.4 An illustration: the failure of the “top-down” applied ethics model
1.0 Introduction 2.0 Objectives 3.0 Main Content
3.1 Kirchhoff’s Current Law 3.2 Kirchhoff’s Voltage Law 3.3
3.4
4.0 Conclusion 5.0 Summary
6.0 Tutor Marked Assignments 7.0 References/Further Readings 1.0 INTRODUCTION
In this unit you will learn about Kirchhoff’s circuit laws also known as Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL).While it is useful to be able to reduce series and parallel resistors in a circuit, circuits are however not always composed exclusively of serial and parallel combinations of resistors. You will recognize that such circuits include star and delta configurations. In such cases you will find it expedient to utilize the powerful set of relations called Kirchhoff's laws which will enable you to analyze arbitrary circuits.
Do you know that the formulas that are used for star to delta and delta to star conversions are derived from Kirchhoff's laws? where the resistances in the three terminal networks are equivalent to the other because they have equivalent resistances across any one pair of terminals.
Kirchhoff's Laws provides the practical means for you to solve for unknowns in a circuit and it makes it possible for you to take a circuit with two or more loops and several power sources and determine loop equations, solve loop currents, and solve individual element currents as Kirchhoff's two laws reveal a unique relationship between current, voltage, and resistance in electrical circuits that is vital to performing and understanding electrical circuit analysis.
17 You are reminded at this point that Kirchhoff's laws only re-affirm the laws governing energy and charge conservation since all of the power provided from the source is consumed by the load. Energy and charge are conserved since voltage and current can be related to energy and charge.
2.0 OBJECTIVES
After reading through this unit, you will be able to
1 State Kirchhoff’s first and second circuit laws
2 Relate Kirchhoff’s current laws to the laws of conservation of charge.
3 Relate Kirchhoff’s voltage laws to the laws of conservation of energy
3.0 MAIN CONTENT
3.1 Kirchhoff’s Current Law
Kirchhoff’s current law states that “The current arriving at any junction point in a circuit is equal to the current leaving that junction” This law is also known as Kirchhoff's point rule,
Kirchhoff's junction rule (or nodal rule), and Kirchhoff's first rule and you are advised to take note that they all refer to Kirchhoff’s current law At any given node of an electrical circuit, the principle of conservation of charge stipulates that the sum of current which flows into the node should equal the sum of current flowing out of it as there can be no accumulation of current. In other words, the algebraic sum of currents in a network of conductors meeting at a point is zero. (Assuming that current entering the
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junction is taken as positive and current leaving the junction is taken as negative).
Mathematically, this can be stated as
k = 0
where n is the total number of branches with currents flowing towards or away from the node.
You will see that this relationship is also valid for complex currents and is signed which takes into account currents flowing towards the node (positive) and current flowing away from the node (negative).
It is easy to see how charge is conserved by Kirchhoff’s current law when you recall that charge (measured in coulombs) is the product of the current (in amperes) and the time (which is measured in seconds).
3.2 Kirchhoff’s Voltage Law
Kirchhoff’s voltage law states that that “The sum of the voltage drops around a closed loop is equal to the sum of the voltage sources of that loop”. This law is also known as Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule and you are again advised to note that they all refer to Kirchhoff’s voltage law.
Mathematically Kirchhoff’s voltage law can be stated as
k = 0
where n is the total number of voltages measured.
19 Once again, this relationship is also valid for complex currents and is signed which takes into account voltage polarities along the loop trajectory.
Kirchhoff’s voltage law is based on the conservation of energy given/taken or energy taken by potential field excluding energy taken by dissipation. A charge which has completed a closed loop does not gain or lose energy for a given voltage potential. It simply goes back to initial pot ential level.
The law is valid even with energy dissipating resistance in the circuit as electrical charges do not return to their starting potential due to energy dissipation but just terminate at the negative terminal instead of positive terminal. This means all the energy given by the potential difference is been fully dissipated by resistance in the form of heat.
Kirchhoff's voltage law is a law relating to potential generated by voltage sources regardless of the electronic components which are present in the circuit whereby the gain or loss in "energy given by the potential field"
must be zero when a charge completes a closed loop.
4.0 CONCLUSION
We learnt in Unit 2 that Kirchhoff’s circuit laws are as a consequence of the laws of conservation of energy and electrical charge, and that many of the other specialized theorems and laws of electrical network analysis are derived from them.
5.0 SUMMARY
- Kirchhoff’s Current Law can be stated mathematically as
k = 0
- Kirchhoff’s Voltage Law can be stated mathematically as
k = 0
- Star and delta electrical networks configurations are best analysed by using Kirchhoff’s laws
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6.0 TUTOR MARKED ASSIGNMENTS 1. State Kirchhoff’s Current law
2. Give two other common names by which Kirchhoff’s Voltage law is known?
3. In the diagram below, what is the value of the current i4 if i1, i2
and i3 are 7, 15 and -18 milliamps respectively, and taking current directed towards the node as being positive in value?
4. What is the voltage across R2 if the voltages across R1 and R3 are 3 volts and 5 volts respectively? The source voltage is 12 volts.
7.0 REFERENCES/FURTHER READINGS Electronic Devices and Circuit Theory 7th Edition
By Robert E. Boylestad and Louis Nashesky Published by Prentice Hall
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Network Analysis with Applications 4th Edition By William D. Stanley Published by Prentice Hall Fundamentals of Electric Circuits 4th Edition
By Alexander and Sadiku Published by Mc Graw Hill
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UNIT 3 COMPLEX IMPEDANCES