Lec03 - Basic Laws

8/12/2019 Lec03 - Basic Laws

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P R E P A R E D B Y :

E N G R . D E A N M A R T S . A N C H E T A

Basic Laws


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Introduction

Chapter 1 introduced basic concepts such as current, voltage,and powerin an electric circuit.

To actually determine the values of these variables in a given circuitrequires that we understand some fundamental laws that governelectric circuits. These laws, known as Ohms law andKirchhoffs laws,form the foundation upon which electric circuitanalysis is built.

In this chapter, in addition to these laws, we shall discuss sometechniques commonly applied in circuit design and analysis. Thesetechniques include combining resistors in series or parallel,

voltage division, current division, and delta-to-wye andwye-to-delta transformations.The application of these lawsand techniques will be restricted to resistive circuits in this chapter.

We will finally apply the laws and techniques to real-life problems ofelectrical lighting and the design of dc meters.


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Ohms Law

It should be pointed out that not all resistors obeyOhmslaw.

A resistor that obeys Ohmslaw is known as a linear

resistor. It has a constant resistance and thus itscurrent-voltage characteristic is as illustrated in Fig.2.7(a): its i-v graph is a straight line passing throughthe origin.


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Ohms Law

A nonlinear resistor does not obey Ohms law. Itsresistance varies with current and its i-v characteristic istypically shown in Fig. 2.7(b).

Examples of devices with nonlinear resistance are thelightbulb and the diode. Although all practical resistorsmay exhibit nonlinear behavior under certain conditions,

but during our discussion we will assume that allelements actually designated as resistors are linear.


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Ohms Law

We should note two things:

1. The power dissipated in a resistor is a nonlinearfunction of either current or voltage.

2. Since R and G are positive quantities, the powerdissipated in a resistor is always positive. Thus, aresistor always absorbs power from the circuit. Thisconfirms the idea that a resistor is a passive element,

incapable of generating energy.


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Sample Problem

1.

2.


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Nodes, Branches, and Loops

A branch represents a single element such as a voltagesource or a resistor.

A node is the point of connection between two or morebranches.

A loop is any closed path in a circuit.


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As the next two definitions show, circuit topology isof great value to the study of voltages and currents inan electric circuit.

Two or more elements are in series if theyexclusively share a single node and consequentlycarry the same current.

Two or more elements are in parallel if they are

connected to the same two nodes andconsequently have the same voltage across them.


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Sample Problem

5. Determine the number of branches and nodes inthe circuit shown in Fig. 2.12. Identify whichelements are in series and which are in parallel.


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Sample Problem

6. How many branches and nodes does the circuit inFig. 2.14 have? Identify the elements that are inseries and in parallel.


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Kirchhoffs Laws


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Kirchhoffs Laws

Kirchhoffs voltage law (KVL) states that thealgebraic sum of all voltages around a closed path (orloop) is zero.

where M is the number of voltages in the loop (or thenumber of branches in the loop) and Vm is the mth

voltage.


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Kirchhoffs Laws

Sum of voltage drops = Sum of voltage rises


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Problem Solving

7.


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Sample Problem

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Sample Problem

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Sample Problem

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Series Resistors and Voltage Division

The equivalent resistance of any number of resistorsconnected in series is the sum of the individualresistances.


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Parallel Resistors and Current Division

The equivalent resistance of two parallel resistors isequal to the product of their resistances divided bytheir sum.


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Parallel Resistors and Current Division

The equivalent conductance of resistors connected inparallel is the sum of their individual conductances.

Current Division


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Sample Problem

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Sample Problem

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Sample Problem


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Sample Problem


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Wye-Delta Transformations

Situations often arise in circuit analysis when theresistors are neither in parallel nor in series. Forexample, consider the bridge circuit in Fig. 2.46.

How do we combine resistors R1 through R6 when the

resistors are neither in series nor in parallel?

Many circuits of the type shown in Fig. 2.46 can besimplified by using three-terminal equivalent networks.


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Delta to Wye Conversion


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Wye to Delta Conversion


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Lec03 - Basic Laws