Eee141 Lab Manual

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Experiment 1

Name of the Experiment:Voltage, Current and Resistance Measurements (Simple Circuit)

1.1 Objective:

The objectives of this experiment are to measure voltage, current and resistance of a simple electric circuit using DMM (Digital Multimeter). These require knowledge of measurement techniques of voltage, current and resistance of a electric circuit.

1.2 Introduction:

The digital multimeter (DMM) is one of the most useful device to measure voltage, current and resistance. Comparing to the analog multimeter, digital multimeter gives us easy to read (seven segment digits) and parallax error free measurement values. DMM can measure AC and DC voltages as well as currents. Every DMM has manufacture specification. This manufacture specification tells us the lower range and the upper range of values it can measure. Suppose if we are planning to measure AC current then the manufacture specification will tell us what is the highest and lowest value of both amplitude and frequency of the current up to which we will able to measure.

Most of the DMM has three terminals and two probes. One terminal is black (zero potential/Ground) and other two terminals are red. One red terminal is for measuring voltage and another one for current. One probe is continuously connected to black terminal and another probe connects to one of the two red terminals depending on the measurement mode. Recently some advance DMM can also measure capacitance, inductance, detect terminals of transistors etc.

To avoid damage of DMM, before connecting the DMM, the measurement mode must be selected and its meter range should placed to its highest value.

In this experiment, the measurement of current, voltage and resistance will be performed by DMM.

1.2 Theory Background:

1.2.1 Voltage Measurement:

Voltage is measured across the circuit elements / components. That is - a parallel connection is made with DMM and the desired element. Voltage measurement requires negative and positive polarity consideration. If the reading gives a positive value the the polarity consideration is correct.

1.2.2 Current Measurement:

Current is measured through the circuit components. So, current measurement requires series connection with the DMM. Current measurement also requires polarity consideration. Similar to voltage measurement a positive reading will indicate right current flow consideration.

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1.2.3 Resistance Measurement:

Resistances are the most simplest form of circuit components. Commercially resistors comes in many shapes, sizes. Most common type of resistors are color coded carbon composition or cabin film resistors. Color codes are multi-colored bands that determines the resistors value and tolerance. To measure the resistance two probes of DMM are connected two ends of the resistor. Again resistance mode (Ohm meter) must be selected before start measuring.

Another way of measuring resistance is reading color code (printed colored rings) on the resistors. One example of color code calculation for axial lead resistor is given in figure 1.1.

Figure: 1.1

Mathematically coded resistance can be expressed as-

R[ohm ]=AB×10C

For five color band resistors the first three are the first three numbers and the fourth one is the multiplication factor.

For radial lead resistors (not very popular in use) the color equivalent numerical values are same as axial lead resistors but the color code arrangement is different (radial lead resistors have no band 5 and band 6 color ). Figure 02 shows a radial lead resistors with color code arrangement.

Figure: 1.2

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So, the calculated resistance of this resistor is - R[ohm ]=AB×10C

1.3 Apparatus:

i.Bread Boardii.Four Resistancesiii.DMMiv.DC Voltage Sourcev.Wires

1.4 Procedure:

i.Construct the resistive circuit according to the figure 1.3 . Place the four resistance in any order.ii.Using DMM fill in the second column (Measured) table 1.1 on next page.iii.After measurement fill in the third column of the table 1.1 using color code reading (for the resistance) and proper theory for measuring voltage and current.iv.Compare the calculated value and measured value by finding the percentage of error. Take calculated value as the ideal value.v.Write down the precautions and conclusion for this experiment in their respective fields.

Figure 1.3

R4R3

R1 R2

+ V2 -+ V1 -

+V3

-

+V4

-

+V -

I1 I2

I3

I4

A B C

D

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Table: 1.1Parameters /Variables Measured Calculated Percentage of Error

(%)R1 (Ώ)R2 (Ώ)R3 (Ώ)R4 (Ώ)i1 (mA)i2 (mA)i3 (mA)i4 (mA)v1 (V)v2 (V)v3 (V)v4 (V)P1 (W)P2 (W)P3 (W)P4 (W)

ΣPdev (W)ΣPdiss (W)

1.6 Calculation: P.E.=∣Calculated value−Measured value∣Calculated value ×100 %

1.7 Precautions:

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1.7 Conclusions:

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Experiment 2

Name of the Experiment: Verification of Kirchhoff's Voltage Law (KVL).

2.1 Objective:

The objective of this experiment is to prove Kirchhoff's Voltage Law (KVL) though both theoretical calculations and experimental measurements.

2.2 Introduction:

Circuit analysis is a process by which each and every elements and nodes are specified by some common parameters (such as voltage, current and resistance). Ohm's Law is the one of the most basic law for circuit analysis. It actually deal with individual circuit elements. The law helps us to determine the voltage across the circuit element or current through it or resistance. Another two laws (KVL and KCL) given by Kirchhoff mainly deals with the interconnectivity of the elements rather than individual elements in a circuit. This behavior of interconnectivity between elements in the circuit helps use to design new circuit for desired need of any circuit element. In this experiment Kirchhoff's Voltage Law will be examined by investigating the behavior of a given simple circuit.

2.3 Theory Background:

Kirchhoff's voltage law expresses the voltage relation across every circuit elements in a closed loop lumped circuit. It says-”the algebraic sum of all the voltages across a closed circuit is zero”.

∑V i = 0

2.3 Apparatus:

i.Bread Boardii.Five Resistorsiii.DMMiv.Wiresv.One DC Voltage Source

2.4 Procedure:

i.Construct the circuit given in figure 2.1. Place eight resistors that are provided in any order.ii.Record the given parameters to appropriate location in table 2.1 by measurement from the constructed circuit. Parameters in the table 2.1 are marked in the in the given circuit in figure 2.1. Calculate theoretical values and compare.iii.Identify the loops and meshes in the circuit. List them in the conclusion part.iv. Using table 2.2 apply KVL on all possible loops using recorded values from table 2.1.v.Write down relevant precautions and conclusion of this experiment in appropriate blank space.

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Figure 2.1

Table 2.1Variable Calculated values Measured Values

v1 (V)v2 (V)v3 (V)v4 (V)v5 (V)

Table 2.2Mesh abea

vab

vbe

vea

Sum

Mesh cdecvcd

vde

vec

Sum

Mesh bcebvbc

vca

veb

Sum

+ V1 - - V3 + + V5 -

+ V4

-

+ VS2

-

- V2

+

+ VS1

-

R1

R2

R3 R5

R4

R1R1

i1

i2

i3

i4

i5

a b

b11 c11

c

d

ee

e

b1 c1

e

a

8

Loop abceavab

vbc

vca

vea

Sum

Loop bcdebvbe

vcd

vde

veb

Sum

Loop abcdeavab

vbc

vcd

vde

vea

Sum

2.5 Precaution:

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2.6 Conclusion:

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Experiment 3

Name of the Experiment: Verification of Kirchhoff's Current Law (KCL)

3.1 Objective:

The objective of this experiment is to analyze a simple circuit to verify Kirchhoff's current law (KCL). This verification also involves theoretical calculation to compare the parameter values obtain from the measurement.

3.2 Introduction:

Kirchhoff's voltage law gives us the information about voltages across the elements as the are interconnected to each other. The second law Kirchhoff's current law (KCL) gives us informations about current flow through each element interconnected in the circuit. In this experiment is primarily intended to verify KCL.

3.3 Theory Background:

Kirchhoff's current law states that the algebraic sum of all the incoming and outgoing current to and from a specific node is equal to zero.

∑ i j = 0

3.4 Apparatus:

i.Bread Boardii.Five Resistorsiii.DMMiv.Wiresv.One DC Voltage Source

3.5 procedure:i.Construct the circuit given in figure 2.1. Place eight resistors that are provided in any order.ii.Record the given parameters to appropriate location in table 3.1 by measurement from the constructed circuit. Parameters in the table 3.1 are marked in the in the given circuit in figure 2.1.iii.Identify the nodes and supernodes in the circuit. List them in the conclusion part.iv.Using table 3.2 apply KCL on all possible nodes using recorded values from table 3.1.v.Fill up table 3.3 using table 2.1 and table 3.1. vi.Write down relevant precautions and conclusion of this experiment in appropriate blank space.

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Table 3.1Variable Calculated values Measured Valuesi1 (mA)i2 (mA)i3 (mA)i4(mA)i5 (mA)

Table 3.2Node b

i1

i2

i3

Sum

Node ci3

i4

i5

Sum

Supernode b1 c1 c11 b11 b1 i1

i2

-i4

-i5

Sum

Table 3.3Power Dissipated

PR1

PR2

PR3

PR4

PR5

Sum

Power DeliveredPS1

PS2

Sum

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2.5 Precautions:

2.6 Conclusion:

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Experiment 4

Name of the Experiment: Verification of Thevenin's Theorem

4.1 Objective:

To verify Thevenin's theorem by both theoretical and experimental procedure.

4.2 Introduction:

It is sometimes required to change a particular circuit element in a complex circuit. For this change, the whole circuit behaves differently. The currents and voltages are redistributed to each circuit elements according to the basic laws of circuit analysis. It also requires recalculation for determining voltages and currents of the changed elements. If the circuit is a big one then this process becomes time consuming and lengthy. Thevenin's theorem reduces that complexity. Thevenin's theorem applies to a circuit when only one circuit element is changed and all the other circuit elements remain unchanged. The desired circuit that has to be changed is considered as load.

4.3 Theory Background:

According to Thevenin's Theorem, if a two port network consisting only linear circuit elements and voltage / current sources then the whole network can be reduced to a voltage source (Vth) and a resistance (Rth) connecting in series with the voltage source. Figure 4.1 shows a two port network with its Thevenin's equivalent representation.

Figure 4.1

Here Vth is the voltage measured across the two terminals of the network after removing the load resistance and Rth is the appeared equivalent resistance after inactivating the voltage and current sources in the network.

4.4 Apparatus:

i. Trainer Boardii. Resistors (one - 4.7 K, two - 3.3 K, one - 100 K, one – 10 K, one - Rheostat )iii. Wiresiv. Digital Multimeter

Two Port

Linear Network R L

Ith

+-

Rth

RL

Ith

Vth

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Figure 4.2

4.5 Procedure:

i. Construct the circuit in the figure 4.2 on the trainer board.ii. Take 3.3 K and 10 K resistors as loads.iii. Place 10 K first at the load side. Measure the voltage VAB and Ith with the help of DMM.

Record the values in the proper field in the table 4.1.iv. Replace 10 K by 3.3 K resistors. Measure the voltage VAB and Ith with the help of DMM.

Record the values in the proper field in the table 4.1.v. Now disconnect the load resistance RL. Place the DMM at open two port network to

measure VAB, which is the Thevenini's Equivalent voltage. Vth.vi. Disconnect the 13 volt source and make the connection short. Measure the equivalent

resistance Rth placing the Ohm meter at terminals AB.vii. Record these values in the table 4.2.viii. Now set the value of the voltage source in the trainer board equal to Vth.ix. Set the value of the Rheostat equal to Rth and connect it in series with the voltage source.x. For fill up table 4.3 first place 10 K resistor and then place 3.3 K in series with the V th

and Rth and measure the voltage VAB and Ith for both the load resistors.xi. Compare table 4.1 and 4.3.xii. Write down the necessary precautions in the section 4.6.xiii. In section 4.7 write down the conclusion of this experiment. Mention the

objectives whether they are achieved or not. Also calculate the percentage of error in the experiment while comparing table 4.1 and table 4.3. Explain why this percentage of error showed up.

IthIth

A

B

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Table 4.1Load Resistance (Ω) VAB (Volt) Ith (mA)

Table 4.2Vth (Volt) Rth (Ω)

Table 4.3Load Resistance (Ω) VAB (Volt) Ith (mA)

4.6 Precaution:

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4.7 Conclusion:

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Experiment 5

Name of the Experiment: Verification of Superposition Theorem

5.1 Objective:

The objective of this experiment is to verify Superposition Theorem using multi source linear circuit. This experiment also demand theoretical analysis of the same circuit using Superposition theorem.

5.2 Introduction:

Like other circuit theorem Superposition Theorem very much applicable in circuit where multiple power supply are used. This theorem determines voltages and currents of different circuit elements for individual power sources.

5.3 Theory Background:

The Superposition Theorem states that total current through or voltage across any branch of multi powered linear circuit equals the algebraic sum of the currents and voltages produced by each source acting separately throughout the circuit. To realize the influence of a particular power source (voltage/current) on a desired branch of a circuit all the power sources must be made inactive (make it short for voltage sources / make it open for current sources. Except for all the sources, in turn, the same procedure is followed. The addition of the results for certain element finally gives the total influence of all the sources activated simultaneously.

5.4 Apparatus:

i. Trainer Boardii. Digital Multimeteriii. Resistorsiv. Wiresv. Three Voltage Sources

Figure 5.1

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5.5 Procedure:

i. Construct the circuit given in figure 5.1 .ii. Measure the voltage across and current through the load resistor RL. Record these values in

appropriate places in table 5.1.iii. Now to determine the influence of voltage source V1 deactivate voltage source V2 and V3 by

disconnecting V2 and V3 then join two terminals for each of them in the circuit in order to make it short.

iv. Measure the current and voltage for the load. Record these values in table 5.2.v. To measure the influence of voltage sources V2 and V3 follow procedure iii and iv twice.vi. Record all the measures values in the given tables.vii. Solve the circuit theoretically in the section 5.6 (Calculation). viii. Write down the precautions relevant to this experiment.ix. Write down the conclusion for this experiment mentioning the objectives, experimental

results. Compare the result from the table 5.1 and table 5.2. Calculate the percentage of error in the comparison. Also compare the theoretical result obtained from the section 5.6 and experimental results.

Table 5.1VL (Volt) IL (mA)

Table 5.2

Active Source VL (Volt) IL (mA)Sum

VL = VL1+VL2+VL3

(Volt)

Sum IL = IL1+IL2+IL3

(mA)V1 Activated VL1| IL1|V2 Activated VL2| IL2|V3 Activated VL3| IL3|

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5.6 Calculation:

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5.7 Precaution:

5.8 Conclusion:

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Experiment: 6

Name of the Experiment:Verification of Maximum Power Transfer and Graphical Analysis of Circuits.

6.1 Objective:

The objective of this experiment is to verify maximum power transfer theorem with graphical analysis.

6.2 Introduction:

In a two port linear circuit, it is desired to find what load can receive maximum power from the circuit. Any two port network can be represented by Thevenin's equivalent circuit. That is a voltage source, a resistor and a load all are in series.

6.3 Theory Background:

The Maximum Power Transfer Theorem states that – a load will receive maximum power from a network when the load resistance is exactly equal to the Thevenin's resistance.

Figure 6.1

In this figure (figure 6.1) the load resistance will get highest power supply if - RTh=RL . Using the figure 6.1 the current through the each resistor is -

I L =V Th

RThRL=

V Th

RThRTh=

V Th

2 RTh

Then the power equation becomes,

P L = I L2 RL =

V Th

2 RTh2

RTh =V Th RTh

4 RTh2

or, P L Max =V Th

2

4RTh

+-

Rth

RL

Ith

Vth

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Note: If the load applied is less than the Thevvenin Resistance, the power to the load will drop off rapidly as it gets smaller. However, if the applied load is greater than the Thevenin Resistance, the power to the load will not drop off as rapidly as it increases.

6.4 Apparatus:

i. Resistances (one - 4.7 KΩ, one - 10 KΩ, one - 100 KΩ, two – 3.3 KΩ)ii. Trainer Boardiii. Digital Multimeteriv. Wires

Figure 6.26.5 Procedure:

i. Construct the circuit given in the figure 6.2.ii. Find out the Thevenin's Equivalent Two port network considering the load resistance RL. For

this part students can take a review from experiment 4.iii. Record the Thevenin's Voltage and Resistance in the table 6.1.iv. Set the Thevenin's Equivalent circuit in the Trainer Board along with a Rheostat.v. Start with different values of load resistance in increasing order in a long range. The range

should cross the value of Rth. Measure the voltage across the load resistance for each values. Record them in the table 6.2.

vi. Calculate the power in the table for each load resistance values.vii. Determine the load resistance for which the maximum power transfers to the load.viii. Plot the graph for power vs. load resistance in the section 6.6.ix. Theoretically analyze the given circuit and determine the maximum power and its

requirements in the section 6.7. x. Write down the precautions that must be taken during the experiment in the section 6.8.xi. Write down the conclusion (section 6.9) of this experiment. Mention what is the objective

was, how much of the objectives are fulfilled, calculate the errors occurred in the experiment (compare the measurement values with calculated values), reasons for the errors etc..

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Table 6.1Thevenin's Voltage Thevenin's Resistance

Table 6.2Serial No. Load Resistance

(KΩ)Voltage Across the Load Resistance

(Volt)

Power transfer to the Load (Watt)

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6.6 Graphs:

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6.7 Precaution:

6.8 Conclusion:

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Experiment No: 7

Name of the Experiment:Introduction to the Basic Properties Alternating Current (AC) Waves.

7.1 Objective:

The objective of this experiment is to study AC (sine) waves and measure its frequency, amplitude and phase then compare the values to another sine wave using oscilloscope. This experiment also requires to measure the effective r.m.s value of the supplied voltage and current.

7.2 Theory Background:

Any periodic variation of current or voltage where the current (or voltage), when measured along any particular direction, goes positive as well as negative, is defined to be an AC quantity. Sinusoidal AC wave shapes are the ones where the variation (current or voltage) is a sine function of time.

Figure: 7.1

For the wave form in figure 7.1,

Time period = TFrequency f = 1/T

Effective value:

Effective (r.m.s) values of sinusoidal waveforms are given as:

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0

2 mT V

dtvT

V == ∫ (For sinusoidal wave)

21

0

2 mT I

dtiT

I == ∫ (For sinusoidal wave)

v

Vm

t

T

tTVftVv )/2sin(2sin ππ ==

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These values are directly measured in ac voltmeter / ammeters and can be used in power calculation as:

RVRIP /22 ==

Phase Difference:

Figure 7.2

Phase difference between two ac sinusoidal waveforms is the difference in electrical angle between two identical points of the two waves. In fig. 2, the voltage and current equations are given as:

tTSinVv m )/2( π=)/2( θπ −= TtSinIi m

Relation between the voltage across and the current through any component of an ac circuit is given by impedance. For the voltage and current waveforms in Fig. 2, the corresponding impedance Z is given as:

θθ ∠=∠= rmsrmsmm IVIVZ //

7.3 Apparatus:

i. Oscilloscopeii. Function Generatoriii. Capacitor (1 μF)iv. Resistor (100 KΩ)v. Digital Multimetervi. Trainer Board

v/i

tθ

T

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Figure 7.3

7.4 Procedure:

i. Connect the output of the function generator directly to channel 1 of the oscilloscope as shown in figure 7.3. Set the amplitude of the wave at 10V and the frequency at 1 kHz. Select sinusoidal wave shape.

ii. Sketch the wave shape observed on the oscilloscope. Determine the time period of the wave, calculate the frequency and r.m.s voltage.

iii. Measure the voltage with an AC voltmeter and compare with oscilloscope result.iv. Change the frequency to 500 Hz and 2 kHz. Note time period.

7.5 Data:

• Time Period of Sine Wave =• Frequency of the Source Voltage =• Amplitude (peak – to – peak) of the Source Voltage =• R.M.S Value of the Source Voltage (from oscilloscope) =• R.M.S Value of the Source Voltage (From voltage) =

6.7 Precaution:

~ Vp-pChannel 1 (Oscilloscope)

AC

Vol

tage

Sou

rce

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6.8 Conclusion: