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Experiment 4 Thevenin’s Theorem and Power Transfer John Nosek ENEE 206 Section 101 Lab Report 4 3/9/04 ● Objective To study Thevenin’s Theorems and use different ways to find Thevenin resistance and Thevenin Equivalent circuits. Also to study power transfer in circuits. ● Equipment - DC Power Supply - Digital Multimeter - Breadboard - 20 kΩ Potentiometer - Following Resistors: 500 Ω 1 kΩ 1.5 kΩ 3 kΩ 2 x 5 kΩ 6 kΩ 7.5 kΩ 2 x 10 kΩ 33 kΩ 62 kΩ 100 kΩ ● Schematics Figure 1 R2 R5 V12 a R1 = 1 kΩ R2 = 5 kΩ R3 = 5 kΩ R4 = 10 kΩ R5 = 7.5 kΩ R4 R1 R3 V12 = 12 V DC V6 = 6 V DC V6 b ● Procedure Part A involved constructing the circuit in Figure 1 and taking certain measurements on it to develop the Thevenin Resistance and Equivalent. First, the actual values of the resistors in the circuit were measured and recorded. The circuit was then constructed and the open circuit voltage and short circuit current was measure so the Thevenin Resistance could be found. Since most circuits will not permit shorting of the output terminals, we used another method to find the Thevenin Resistance. The potentiometer was connected as a load between terminals a and b and adjusted till the voltage across it was half of the open circuit voltage. The resistance of the potentiometer was then taken since it was then equal to the Thevenin Resistance. Using a known resistor, it was then connected between terminals a and b and the voltage drop across it was measured so the Thevenin Resistance could be calculated a third way. With the same resistor still in the circuit, the current through the resistor was measured so another calculation of the Thevenin Resistance could be made. The voltage sources were then zeroed out and the resistance at the terminals was measured for a final measurement of the Thevenin Resistance. Finally, the results were compared and a schematic for the Thevenin Equivalent Circuit was drawn. Part B involved measuring the power transfer in the circuit in Figure 1. The voltage at terminals a and b was measured along with the actual values of the remaining resistors. All the load resistors were then placed across terminals a and b and the voltage across them was measured so the power dissipated could be calculated. By plotting the power dissipated versus the load resistance, the Thevenin Resistance was found again. This value was compared to the values obtained in Part A. ● Results Part A 1) Resistor R1 R2 R3 R4 R5 3) Marked Value 1 kΩ 5 kΩ 5 kΩ 10 kΩ 7.5 kΩ Vopen 5.990 V I short 0.51 mA Measured Value 0.995 kΩ 5.057 kΩ 5.050 kΩ 10.15 kΩ 7.360 kΩ RTH Vopen RTH 5.990 11.745 k 0.00051 4) 5) 6) I short RTH R p 12.06 k R 10.01 k Vab 2.725 V Vopen 5.990 V Vopen RTH R Vab R 5.990 2.725 2.72 10 4 RTH 10010 10010 RTH 7) 5.990 10010 11.99 k 2.72 10 4 Vopen 5.990 V R 10.01 k I R 0.28 mA RTH Vopen IR R 5.990 10010 11.38 k .00028 RTH measured with sources zeroed out 12.02 k 8) After comparing the results, it seems that all calculations point to a value for the Thevenin Resistance being around 12 kΩ. This value corresponds to the Thevenin Voltage Source of about 6 V and to all calculations performed. Thevenin Equivalent Circuit 12 kΩ a 6 V DC b Part B 1) Vopen 5.991 V 2) Resistor Values Marked Value 500 Ω 1.5 kΩ 3 kΩ 6 kΩ 10 kΩ 20 kΩ 30 kΩ 62 kΩ 100 kΩ Measured Value 507.5 Ω 1.474 kΩ 2.970 kΩ 6.076 kΩ 10.01 kΩ 19.82 kΩ 32.71 kΩ 61.31 kΩ 98.2 kΩ 3, 4, 5) Resistor 500 Ω 1.5 kΩ 3 kΩ 6 kΩ 10 kΩ 20 kΩ 33 kΩ 62 kΩ 100 kΩ Voltage Load VL 0.243 V 0.654 V 1.186 V 2.011 V 2.723 V 3.729 V 4.381 V 5.009 V 5.337 V Power Dissipated (V2/R) .116 mW .290 mW .474 mW .665 mW .741 mW .702 mW .587 mW .409 mW .290 mW 6) Power Dissipation In Resistors 0.8 0.7 Power (mW) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 20000 40000 60000 Resistance (Ω) 80000 100000 7) Based on the fact that the maximum power transferred is at the load resistance equal in value to the Thevenin Resistance: RTH 11 k 8) This answer and the graph closely represents the values obtain in Part A which proves the relationship between resistance and power dissipation. ● Conclusion This lab experiment showed many methods used to find the open circuit voltage, close circuit current, and Thevenin Resistance needed in order to develop a Thevenin Equivalent Circuit for a given circuit. Most importantly, it showed the many calculations that can be done to obtain the Thevenin Resistance and what measurements are needed to be known in order to perform them. It clearly showed the many relationships involved in Thevenin Circuits. Also, the final part of the lab showed the relationship that exists between Thevenin Resistance and the maximum power dissipation in a circuit.