Electrical Systems 100 Lab 2

Laboratory No 2 Electrical Systems 100

ELECTRICAL SYSTEMS 100

STUDENT NUMBER: 13952673

NAME: AJ PERKS

GROUP: A5 THURSDAY (08:00am)

LABORATORY: 2. DC CIRCUITS

LABORATORY SUPERVISOR: KEITH RAINBOW

LABORATORY PARTNERS: JIMMY

DATE PERFORMED: 13 AUGUST 2009

DATE DUE: 26 MAY 2004

DATE SUBMITTED: 26 MAY 2004

I hereby declare that the calculations, results, discussion and conclusions submitted in this report are entirely my own work and have not been copied from any other

student or past student.

……………………………………………………(AJ PERKS)

13952673 AJ Perks


DC Circuits

Introduction

The purpose of this laboratory was to analyse direct current (DC) circuits using different techniques. These included using fundamental laws from Kirchoff and Thevenin to predict the performance of power networks and DC circuits.

Summary of results

Circuit 2.1 the voltages for the circuit varied by 4.13% and the current measured was only 0.04% different from the theoretical values. In circuit 2.2 there was a abnormally large difference of 37.23% and the voltage varied by 0.02%. Circuit 2.3 results for current, voltage and power varied by 8.8%, 10.51% and 15.41% on average respectively. The graph load power against normalised resistance when graphed showed a parabolic relationship which was desired. The last circuit, circuit 2.4 the results for voltage and current varied by 0.83% and 4.21% on average respectively.

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Circuit 2.1

Figure 1

Results

2.1 Voltage (volts) Current (Amps)Measured Theoretical Experimental Theoretical ExperimentalR1 15 14.38 0.031940 0.031860R2 15 14.38 0.015000 0.015060R3 15 14.37 0.010000 0.010100Supply 15 15 0.056914 0.056890

Circuit 2.2 and 2.3

Figure 2 Figure 3.(Thevenin Equivalent)

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Results

2.2

Measured E1 (volts) E2 (volts) I (Amps) PL (watts) VRL (volts)

Experimental 9.0100 20.0000 0.0905 x 4.6570

Theoretical 9.0000 20.0000 0.0568 0.2644 4.6560

2.3 Load Voltage (volts) Current (amps) Power (watts)ohms Theoretical Experimental Theoretical Experimental Theoretical Experimental

10 0.8395 1.0040 0.0859 0.0850 0.0739 0.077382 4.6559 5.2200 0.0568 0.0635 0.2643 0.3302

100 5.2338 5.7400 0.0522 0.0569 0.2739 0.3238130 6.0194 6.5180 0.0463 0.0502 0.2787 0.3271150 6.4497 6.9600 0.0429 0.0462 0.2773 0.3201220 7.5684 8.0300 0.0345 0.0365 0.2604 0.2923

1000 10.6580 10.8400 0.0107 0.0109 0.1136 0.1179

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Graphs

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Circuit 2.4

Figure 4

Results

2.4 Voltage (volts) Current (amps)Measurement Theoretical Experimental Theoretical ExperimentalR1 3.9135 3.9900 0.0261 0.0265R2 12.1721 12.0700 0.0148 0.0147R3 1.3499 1.1780 0.0112 0.0118R4 5.5466 10.8900 0.0230 0.0210R5 -1.7770 -1.1240 -0.0118 -0.0210R6 3.9139 3.9450 0.0261 0.0179point 1 16.0830 16.0600 0.0261 0.0250point 2 12.1721 12.0700 0.0148 0.0137point 3 10.8260 10.8900 0.0230 0.0217point 4 3.9139 3.9450 0.0261 0.0231point 5 0.0000 0.0000 0.0148 0.0146

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Discussion

In circuit 2.1 the experimental and theoretical results were quite close, the voltages for the circuit were 4.13% away from 15V. The current measured was only 0.04% different from the theoretical values. Reasons for variations between experimental values and theoritical values could be due to human error, faulty equipment and also when the temperature of the conductor increases, the collisions between electrons and atoms increase. This means the resistor heats up because of electricity flowing through it and the resistance will increase. This would give a false reading on the multimeter if the circuit had been left on for to long.

Circuit 2.2 the current was very different between the theoretical and experimental result this is due to in the pre lab questions perhaps my calculated theoretical result is wrong due to the large difference of 37.23%. The voltages on the other hand were only 0.02% apart.

The graphs for load power verse normalised resistance in circuit 2.3 do follow the parabolic shape. This is the desired graph that should be seen. Although I did not graph the log of load power against the normalised resistance but the load resistance verse the log of load power instead it can be seen that max value is roughly at the RTh

value of 130.15. This also is desired in the graphed results. The experimental results graph it can is seen that it does not have a dome at the top that is a characteristic of a parabola type graph. This could be due to human errors. Setting up the circuit 2.3 was quit difficult and possibly could be wrong giving higher readings for the values of current and voltage and therefore power as it can be seen on average the power was 15.41% different from the theoretical and experimental values.

The voltage over resistor four was vastly different being nearly double the theoretical value. This can most likely be reduced to human error when measuring the voltage over resistor four since none of the other results in circuit 2.4 were this different between theoretical and experimental results.

Conclusion

The experiment was a success it showed a parabolic relationship between load power and normalised resistance. The graphed showed that the maximum value was roughly at the RTh value of 130.15 which is desired.

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Appendices

Circuit 2.1 calculations:

Example of total resistance (RT):

Example of current drawn from the supply (Is):

Example of current through a resistor (IR1):


Figure 5

Example to find the voltage drop across the load resistance (RL):Using Nodal analysis from VB

Example to find the current through RL:

Example to calculate the load power (PL):

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Figure 6

Example of calculating RTh:

Example of calculating VTh:

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Example to find the current in circuit 2.4:

Figure 7Using mesh analysis with 3 loopsLoop 1

Eq1

Loop 2

Eq2

Loop 3

Eq3

Using Eq1,2 and 3 set up a matrix ,,

1120 -820 0 20-820 1410 -470 0

0 -470 570 -12

Solving the above matrix:I1=0.0260928I2=0.0112488I3=-0.01177727968

Calculating the voltage drop across resistor 2 (VR2):

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Calculating the current through resistor 2 (IR2):

Calculating the Voltage at point 2 (VPT2):Using nodal analysis

Calculating the current at point 2 (IPT2):

References

Boylestad Introductory circuit analysis 11th edition Prentice Hall

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Pre-lab

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Lab test result

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Documents

Electrical Systems 100 Lab 2