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The objectives of this experiment are to Verify Kirchhoffs laws Determine the equivalent resistance of a network & Study the maximum power transfer theorem.

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Introduction

EE2721 Electric Circuit Analysis

Group 5

Introduction:

The objectives of this experiment are to

Verify Kirchhoff’s laws

Determine the equivalent resistance of a network

Study the maximum power transfer theorem

Apparatus:

DC power supply

Multi-meter (DMM)

Experimental board

Experiment 1:(Kirchhoff’s laws)

Theory:

According to the Principle of conservation of Charges, since charges do not accumulate at any point in a network, the charges cannot be created or destroyed.

This bring the Kirchhoff’s First Law, the algebraic sum of the current at a junction of a circuit is zero. Therefore, the current arriving a junction equals the current leaving the junction.

image00.png

This law also assumed to be positive if it flows into a point and negative if it flows out from the point.

There is also a Kirchhoff’s second law relates the total e.m.f in a closed loop.

Round a closed loop, the algebraic sum of the e.m.

...read more.

Middle

=21.5Ω

The power supply was removed, we measured again the equivalent resistance image21.png

=28.4Ω

The result in step 1 is smaller than in step 2.In step 1 , the power supply has not been removed, and it consists internal resistance. As it connects parallel to

the circuit, the equivalent resistance will be smaller than without parallel internal resistance.

The star-to delta or the delta –to –star transformation was used to calculate the equivalent resistance of network shown in figure 3.

image22.png

image23.png

image24.png

image25.png

image26.png

image27.png

equivalent resistance of image21.png

:

image28.png

The image21.png

we calculate is close to step 1 but smaller than step 2. When we calculate the equivalent resistance of image21.png

,we don’t know the internal resistance of power supply and we assumed the internal resistance is zero and ignore it in calculation, so the result we calculate is similar to data with removal of power supply.

Experiment 3(Maximum power transfer theorem)

Procedures:

The circuit as shown in figure 7 with image29.png

...read more.

Conclusion

span="1" rowspan="1">

8.909

9.98

11.198

12.475

14.851

image37.png

0.55

0.566

0.573

0.587

0.596

0.612

0.609

0.603

0.601

0.600

Maximum power: 0.6127mW

image38.png

9.2image39.png

Total resistance:9.2+10=19.2image39.png

image33.png

=20KΩ(with image30.png

 varying from 15KΩ to 25KΩ)

image34.png

2.153

2.2155

2.2779

2.3403

2.4028

2.5351

2.5973

2.6597

2.722

2.784

image35.png

0.142

0.1388

0.1357

0.1326

0.1294

0.1265

0.1236

0.1205

0.1174

0.1143

image36.png

15.121

15.962

16.786

17.649

18.569

20.04

21.014

22.072

23.186

24.356

image37.png

0.307

0.308

0.309

0.31

0.311

0.321

0.321

0.32

0.319

0.318

Maximum power: 0.0215mW

image38.png

20.05image39.png

Total resistance:20.05+20=40.05image39.png

Discussion:

aI) minimum sources voltage:

V=400x2ximage40.png

=40v

aII) there is not significant risk of this type of accident to occur, as the voltage of personal computer is 17v, it is smaller than the minimum source voltage that can produce electrical shock.

b) The criterion for maximum power transfer from a source to a load is the load resistance equals to the internal resistance of the source. If we are free to select image33.png

without changing the source voltage, we can decrease the image33.png

 in order to maximize the power delivered to the load.

E=i(R+image41.png

iE=image42.png

image43.png

=image44.png

image43.png

=image45.png

The smaller the image33.png

, the higher the power supply

C)image46.png

=image47.png

      =image48.png

    =image49.png

      The maximum power output occurs when

image50.png

=image51.png

=0

image52.png

=0

image53.png

=2R

image54.png

=image33.png

The maximum power output

image55.png

=image48.png

=image56.png

...read more.

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