cb lab manual cicrcuit laws

7/23/2019 CB Lab Manual Cicrcuit Laws

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EG1108/E2/1

NATIONAL UNIVERSITY OF SINGAPORE

Faculty of Engineering

EG1108 Electrical Engineering

Laboratory Manual

Experiment E2

D.C. Circui t Analysis

Academic Year 2010/2011


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Important Instructions:

You are not allowed to come to the lab with slippers and sandals. You MUST put on

covered shoes.

Bring along logbook. You are not allowed to submit your reports in papers.

Read the experiment manual before you come for the experiment.

Enter the lab on time in order to finish the experiment on time.

Note down all the experimental data directly in your logbook in order to save time

Try to finish the experiment in 2.5 hours. You must submit the logbook (within 3-3.5

hours) with the complete set of experiment readings, answers and discussions before

leaving the lab.

Submit the logbook at the end of the lab session. Place your logbook to the correct

submission box corresponding to your lab session.

1. INTRODUCTION

An understanding of electrical circuits is the core of the material required for a good

introduction to the field of electrical engineering. In several applications, we often

face circuit analysis problems for which the structure of the circuit and element values

are known, and the current, voltages and powers need to be determined. In this

experiment, we gain hands-on experience on techniques for analyzing circuits

composed of resistances, voltage sources and current sources.

One of the most important concepts in circuit analysis is that of equivalent source

representation. The equivalent source may be either a voltage source or a current

source. The equivalent voltage source is called the Thevenin representation, and theequivalent current source is called the Norton representation. Based on these, two

powerful circuit analysis techniques which will be explored are known as Thevenins

theorem and Nortons theorem. Both convert a complex circuit to a simpler series or

parallel equivalent circuit for easier analysis. Analysis involves removing part of the

circuit across two terminals to aid calculation, later combining the circuit with the

Thevenin or Norton equivalent circuit. Principle of superposition theorem and

maximum power transfer will also be introduced via experimentation.

This laboratory experiment will provide the students the opportunity to build,

experiment with, and conduct measurements on basic electrical circuits, and learn to

use theorems and techniques to solve complex electrical circuits. These concepts can

be extended to circuits containing inductances and capacitances.

2. OBJECTIVES

To investigate Kichoffs Laws, Theory of Superposition, Thevenins theorem and

Nortons theorem using linear, resistive circuits.


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3. EQUIPMENT

The experiment will introduce you to modern lab equipment similar to that used in the

industry. In particular, the following will be used:

1. Resistors of various values

2.

Breadboard3.

Digital multimeter

4. Variable D.C. power supply

5.

One set of PC (to be shared by two students)

6. OrCAD Pspice Demo Version 9.1

7. Network Printer

3.1 Variable Resistors

The standard resistor color code is shown in Figure 9 at the end of this manual. Here

is a quick synopsis: Most resistors have four colored bands. The first three bands

indicate the nominal value of the resistor and the fourth band indicates the tolerance in

value. The first two bands form the mantissa, and the third the exponent of 10.

3.2 Breadboard

The solderless breadboard (sometimes called a protoboard) is the most common type

of prototyping circuit board. Prototyping a circuit is the process of creating a model

suitable for complete evaluation of its design and performance. This requires the

circuit to be designed, built and tested in the laboratory. Theoretical calculations and

computer simulation are part of the design process. Once the circuit configuration is

determined, the circuit is built on a prototyping board. Fig. 10 (in the Appendix)

shows the schematic diagram of a breadboard. You will build your circuits on the

terminal strips by inserting the leads of circuit components into the contact receptacles

and making connections with wires.

3.3 Digital Multimeter

The digital multimeter measures voltage, current and resistance. There are separate

settings for measuring A.C. and D.C. values. The multimeter also has the capability of

measuring other quantities such as the frequency and period of periodic waveforms.

The operation of the digital multimeter is almost entirely automatic, simply set the

multimeter to the type of measurement you wish to make by pressing the button

labeled voltage, current, etc. and read the value from the display.

3.4 D.C. Power Supply

The D.C. power supply is used to generate either a constant voltage or a constant

current. That is, it may be used as either a D.C. voltage source or a D.C. current

source. You will be using it primarily as a variable voltage source. D.C. means

constant with respect to time. The D.C. power supply has two range settings. The

voltage produced by the power supply is controlled by the knob labeled voltage. The

current is limited by adjusting the knob labeled current.


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4. THEORY

4.1 Kirchof fs Current Law (KCL)

In the first part of the experiment, we examine series-parallel circuit supplied by D.C.

Power Supply with time-constant electromotive force. The purpose of this experiment

is to experimentally verify Kirchoffs Current and Voltage Laws, and developproficiency in the use of digital multimeter in the context of verifying Kirchhoffs

Laws.

Kirchoffs Current Law states that the algebraic sum of the currents entering (or

leaving) a node (or more generally, a closed surface) at any instant is zero.

Fig. 1 Kirchoffs Current Law

According to KCL, i1+ i2+ i3+ i4+ i5= 0 (1)

Note that in Fig. 1, the directions of arrows indicate the chosen reference current

polarities. Thus, if the i3 reference polarity (arrow direction) is reversed, then eq. (1)

will be re-written as follows.

i1+ i2- i3+ i4+ i5= 0 (1a)

4.2 Kirchof fs Voltage Law (KVL)

The algebraic sum of voltages (potential rise or drop) around a closed loop at any

instant is zero.

Fig. 2 Kirchoffs Voltage Law

Given that vijis the potential drop between the nodes i andj,

Using the arrangement of potential drops in Fig. 2b, the following relation holds good

according to KVL: v21+ v32+ v43+ v54+ v15= 0 (2)


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Using the arrangement of potential drops in Fig. 2c, the following relation holds good

according to KVL: v12+ v23+ v34+ v45+ v51= 0 (3)

Note that in Figs. 2b and 2c, the + and markings across each component indicate the

chosen reference voltage polarities. Thus, in Fig. 2b, if the reference polarity (+ and

symbols) across 2 and 3 is reversed, then eq. (2) will be re-written as follows.

v21- v32+ v43+ v54+ v15= 0 (2a)

or as

v21+ v23+ v43+ v54+ v15= 0 (2b)

4.3 Theory of Superposition

In a linear circuit or network containing several voltage and/or current sources, the

current through any element can be obtained by the algebraic sum of the individual

currents due to each independent source acting alone.

Likewise, in linear circuits, the voltage across any element can be obtained by the

algebraic sum of the individual voltages due to each independent source acting alone.

Note that when we find the voltage or current from one independent source, we kill

the other independent sources (by shorting the independent voltage sources and

opening the independent current sources), but we do not kill other dependent

sources.

Superposition theorem allows us to simplify a complex circuit with many independent

voltage and current sources to a number of simple circuits each containing one

independent source only. This makes the calculation of circuit voltages and currents a

lot easier in many cases.

4.4 Thevenins Theorem

Thevenins Theorem states that it is possible to simplify any linear circuit, no matter

how complex, to an equivalent circuit with just a single voltage source and series

resistance connected to a load. The theorem is applicable to circuits with passive

components (such as resistors, inductors and capacitors). The simplified circuit is

called Thevenins equivalent circuit. Thus, if we wish to find the current in a single

branch of a large circuit, we can leave out the branch and then reduce the remaining

circuit using Thevenins Theorem. This method allows a simple and direct

determination of the current in the desired branch.


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Let us take a look at the example circuit (Fig. 3a). In this example circuit, we see two

voltage sources driving a series-parallel circuit. Let us say that we are interested in

finding out the current through and voltage across the load resistance RLconnected

across points A and B in the circuit. While we have the skills to solve for the load

voltage or load current without too much difficulty, we will use Thevenins Theorem

to solve for the circuit parameter.

Fig. 3a

In general, the Thevenins Theorem allows us to reduce the complex circuit to an

equivalent series circuit consisting only of a single voltage source, V th, a series

resistance, Rthand the load resistance, RL.

To use Thevenins Theorem to solve for the load voltage or current in a circuit, we

first remove the load resistance at terminals A and B, as shown in Fig. 3b.

Fig. 3b

If we look in through the load terminal (i.e. A and B), the remaining circuit can be

viewed as having only one voltage source and one resistance in series with it (Fig. 3e).

In the laboratory, we can place a voltmeter across terminals A and B to measure Vth.

To determine the Thevenins Resistance, Rth, we need to remove all source voltages

and replace them with a short while retaining any internal source resistance; remove

any current sources and replace them with an open circuit while retaining any internal

source resistance; and then look in through terminal A and B and calculate Rth. Fig. 3d

shows the same network as in Fig. 3c with its terminals shorted. If the short-circuit

current is Isc, then the Thevenins Resistance of the network is given by:


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)4(sc

th

thI

VR

Fig. 3c Fig. 3d Fig. 3e

We can calculate this resistance in the laboratory by dividing the voltage across and

current through terminals A and B, as described above. Now that we have determined

the Thevenins Equivalent Resistance and the Thevenins Equivalent Voltage, we

redraw the open circuit as a series circuit consisting of Vthand Rth. In this circuit, we

can now reconnect the load, RLto terminals A and B, and calculate the voltage across

A and B using Ohms Law.

The advantage of using the Thevenins circuit is that we can quickly determine what

would happen to that single resistor if it was of a different value other than that

initially chosen, without having to go through a lot of analysis again.

Thevenins Theorem is especially useful in analyzing power systems and other

complicated circuits where one particular resistor in the circuit (called the load

resistor) is subject to change, and re-calculation of the circuit is necessary with each

trial value of load resistance, to determine the voltage across it and current through it.

Thevenins and Nortons Theorems are also very commonly used in analyzing large

circuits consisting of many stages such as an audio amplifier.

4.5 Norton s Theorem

Nortons Theorem states that it is possible to simplify any linear circuit, no matter

how complex, to an equivalent circuit with just a single current source and parallel

resistance connected to a load.

Nortons Theorem is the dual of Thevenins Theorem. It simplifies a complex

network into a current source called the Norton Current Source IN, a parallel Norton

Equivalent Conductance GNor Norton Equivalent Resistance (RN), and a parallel load

resistance. After creating the Norton Equivalent Circuit (Fig. 4c), you may then easily

determine the load current across terminals A and B.

Nortons equivalent circuit is determined in a manner similar to that used for

Thevenins circuit. As shown in Fig. 4, the open circuit voltage VNat the terminals A

and B of the complicated network (for example, that shown in Fig. 3a), is first

determined as shown in Fig. 4a, and the short circuit current INis calculated as shown

in Fig. 4b. The Nortons conductance of the network is given by eq. (5) below. The

Nortons equivalent circuit of Fig. 4a is shown in Fig. 4c.


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)5(N

N

NV

IG

Fig. 4 Nortons Theorem4.6 Maximum Power Transfer

The reduction of any linear resistive circuit to its Thevenin or Norton equivalent

makes computation of load related quantities very easy. One such computation is the

power absorbed by the load. Given the fact that a practical source has internalresistance, some of the generated power of the source is lost in it.

Fig. 5 Maximum Power Transfer

In order to obtain the value of the load resistance that will absorb the maximum power

from the source, we express the power absorbed by the load as follows:

)6(2 LLL RIP

The load current can be further expressed as:

)7(Lth

th

LRR

VI

Hence, the power absorbed by the load can be re-expressed as:

)8(

2

2

Lth

thL

LRR

VRP

In order to find the value of LR that maximizes LP , we differentiate the equation (8)

with respect to LR to obtain the following:

)9()()(

2

)(

13

2

32

2

Lth

Lth

th

Lth

L

Lth

th

L

L

RR

RRV

RR

R

RRV

dR

dP


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Hence, setting 0L

L

dR

dP, we can see that

Lth RR maximizes LP .

This theorem finds application in the design of electrical circuits where we need to

derive maximum power for a given load by maximizing the current, such as designing

of radio receivers so that the radio receiver can extract maximum signal power from

the receiving antenna.

5. PRE-EXPERIMENT EXERCISES

{Students must do Section 5 prior to coming to laboratory and will not be allowed to

answer these during the 3 hour lab session.}

1.

The following two circuits given are equivalent. What is Vthand Rth?

2.

It is known that voltage source output magnitude is V=10V but it is not know which

terminal have a higher potential. Apply KCL to point C to determine the value of R.

And answer whether the voltage at point B is positive or negative? Take note of the

current flowing direction.

6. EXPERIMENT

6. 1 Application of Theory of Superposit ion

6.1.1 Using the universal colour code shown in Fig. 8 in the Appendix, obtain four different

valued resistors for R1, R2, R3, and R4based on the following list of values (100,330, 390, 470, 560, 680, 750, 820, 910, 1000) and state clearly thechosen resistance values of the resistors in the logbook.

6.1.2 Using the breadboard and the four chosen resistors, patch the simple circuit as shown

in the figure below, with RL = 100. Ensure that the D.C. voltage supplies arecorrectly set according to the specified values in the diagram.

VthRth

+

-Is= 1A

R=10

R R

RR


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Fig. 6 Schematic Circuit Diagram

6.1.3

Apply Kirchoffs Laws and the Theory of Superposition to determine the current IL

flowing through the load resistor (RL).

6.1.4 Connect the multimeter in series with the terminal AB (refer to Fig. 6a). Measure and

record down the actual current IL= IAB= ______ Ausing a multimeter. Is there any

difference between the measured value and the calculated value? If so, why?

Fig. 6a

6.1.5 Verify the Theory of Superposition experimentally by leaving one voltage source in

the circuit at a time (while killingthe other voltage source), and record IL. Compare

these results with those obtained in 6.1.4.

6.2 Application of Thevenins Theorem

6.2.1

Remove the resistor RL and measure the open-circuit voltage Vth of the Thevenins

equivalent across AB (refer to Fig. 6b).

Record down the value of the open-circuit voltage VAB= Vth= ______ V


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Fig. 6b

6.2.2

Short-circuit the terminal AB using a multimeter (refer to Fig. 6c). Record down the

value of the measured current Isc= IAB= ______ A. Hence, calculate the value of the

internal resistance,Rth, of the Thevenin equivalent.

Fig. 6c

6.2.3

Using equation (7) in the Section 4.6, calculate the value of the currentILagain.

6.2.4

Compare this value with the values ofILobtained in Part 6.1

6.2.5

Sketch the Thevenins equivalent circuit based on Vth and Rthdetermined as above.

Using this circuit, determine the load current IL if the value of load resistance RL

connected across terminals AB is now doubled. Experimentally verify this result by

connecting a resistance of double the previously used value of RL. What do youconclude from this?

6.2.6

Connect a load such that RL= Rthand measure the load voltage. Use this to determine

power dissipated in the load. Select two different resistors with resistance greater than

Rth,use one at a time as load, and determine load power for each of them. Then use

two other resistors with resistance smaller than Rthand determine power for each of

them. Plot load power versus load resistance and verify that RL= Rthgives maximum

load power.


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OPTIONAL EXPLORATION

(You may wish to explore further and investigate the application of Nortons theorem. This

exercise is not compulsory.)

6.3 Application of Nortons Theorem

6.3.1 Refer to the circuit shown in Fig. 7. Given that R1= 330, R2= 1 K,R3= 680 and R4 = 100. Apply the Nortons theorem (as seen from the terminals AB,treating R4 as the load resistor) and calculate the Nortons conductance GN (to be

done before the laboratory session).

Fig. 7 Schematic Circuit Diagram

6.3.2 By assigning the values of the resistors according to the given values, connect the

circuit as shown in Fig. 7. Ensure that the D.C. power supply is correctly set to 15V.

6.3.3 Remove the resistorR4and obtain the Norton equivalent across AB of the reminding

circuit as follows:

1)

Connect the multimeter across AB. Measure and record down the open

circuit voltage VN=VAB= ______ V across AB.

2)

Connect a short circuit across AB using the multimeter and record down

the value of the measured currentIN=IAB=______A.

3) Determine the Nortons conductance using equation (5) in Section 4.5.

6.3.4 Compare the value of the Nortons conductance obtained in 6.3.3 with the valueobtained by theoretical calculation in 6.3.1.


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APPENDIX

Identification of resisto r value from color band

Fig. 8 Resistor Colour Code

Table 2: Resistor Colour Code

First Three Bands Fourth Band

Black 0 Blue 6 Gold - 5%Brown 1 Violet 7 Silver - 10%

Red 2 Grey 8 None - 20%Orange 3 White 9

Yellow 4 Silver 0.01

Green 5 Gold 0.1

Structure of breadboard and patching up of a simple circui t

The breadboard will be used as a base on which prototype circuits may be constructed. Fig. 9

shows the schematic diagram of a breadboard. Note the how the different points on the

breadboard are short-circuited or open-circuited to one another. Note the number of terminalstrips, bus strips, and binding posts on your breadboard. Each bus strip has two rows of

contacts. Each of the two rows of contacts on the bus strips are a node. That is, every contact

along a row on a bus strip is connected together, inside the breadboard. Bus strips are used

primarily for power supply connections but are also used for any node requiring a large

number of connections.

Fig. 9 Schematic Diagram of a Breadboard

cb lab manual cicrcuit laws

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