CET 3525 LAB 3 - Laboratory PDF

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Laboratory...

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Lab #3: Thevenin’s Theorem and Maximum Power Transfer.

Date: 10/26/2018

Course and Section: CET 3525-D472

Table of Contents 1. Objectives

2. Equipment

3. Theoretical Background

4. Procedure

5. Data tables

6. Calculations

7. Conclusion

Objectives   

Validate Thevenin’s theorem through experimental measurement. Become aware of an experimental procedure to determine Eth and Rth. Demonstrate that maximum power transfer to a load is defined by the condition RL = Rth

Equipment:    

91 ohms, 220 ohms, 330 ohms, 470 ohms, 1k ohms, 2.2k ohms, 3.3k ohms (1/4W) ---- 1 0-1k ohms potentiometer, 0-10k ohms potentiometer ---- 1 DMM ---- 1 DC Power Supply ---- 1

Theoretical Background: Through the use of Thevenin’s theorem, a complex two-terminal, linear, multisource dc network can be replaced by one having a single source and resistor. The Thevenin equivalent circuit consists of a single dc source referred to as the Thevenin voltage and a single fixed resistor called the Thevenin resistance. The Thevenin voltage is the open-circuit voltage across the terminals in question. The Thevenin resistance is the resistance between these terminals with all the voltage and current sources replaced by their internal resistances.

Procedure: Thevenin Theorem: a) Construct the network of Fig 12.2. Calculate the Thevenin voltage and resistance for the network to the left of points a-a using measured resistor values. Enter the results in Table 12.1. Show all work.

Table 12.1

Calculated Eth Rth

Measured 4.48 2.29

%Difference

b) Insert values of Eth and Rth in Fig 12.3 and calculate IL. Record the results in Table 12.2. c) Calculate the current IL in the original network of Fig 12.2 using series-parallel techniques (use measured resistor values) and insert in Table 12.2. Show all work. d) Turn on the 12- V supply of Fig 12.2, measure the voltage VL and record in Table 12.3. Using the measured value of RL calculate the current IL and record in table 12.3.

Determine Rth: e) Determine Rth by constructing the network of Fig 12. And measuring the resistance between points a-a with RL removed. Record in Table 12.1. f) Determine Eth by constructing the network of Fig 12.5 and measuring the open circuit voltage between points a-a. Record the results in Table 12.1. g) Construct the network of Fig 12.6 and set the values obtained for the measured values of Eth and Rth in parts I(e) and I(f), respectively. Use the ohmmeter section of your meter to set the potentiometer properly. Then measure the voltage VL and calculate the current IL using the measured value of RL. Record both results in Table 12.3. Table 12.3 VL

IL(from VL)

Original network Thevenin equivalent

Maximum Power Transfer (Validating the Condition RL= Rth): a) Construct the network of Fig 12.7 and set the potentiometer to 50 ohms. Measure the voltage across RL as you vary RL through the following values: 50, 100, 200, 300, 330, 400, 600, 800, and 100 ohms. Be sure to set the resistance with the ohmmeter section of your meter before each reading. When setting the resistance level,

remember to turn off the dc supply and disconnect one terminal of the potentiometer. Complete Table 12.4 and plot Pl versus RL on Graph 12.1 terminal of the potentiometer.

Table 12.4 RL 0 ohms 50 ohms 100 ohms 200 ohms 300 ohms 400 ohms 600 ohms 800 ohms 1000 ohms

VL 6V 1.1 V 1.8 V 3.0 V 3.8 V 4.4 V 5.2 V 5.7 V 6.0 V

P = VL/RL (mW)

b) Theoretically, for the network of Fig 12.7, what value of RL should result in maximum power to RL? Record in Table 12.5.

Based on the preceding conclusion, determine VL for maximum power transfer to RL and record in Table 12.5

Set the potentiometer to the resistance RL that resulted in maximum power transfer on Graph 12.1 and measure the resulting voltage across RL. Record in Table 12.5

Maximum Power Transfer (Experimental Approach) a) Construct the network of Fig 12.8. Insert the measured value of each resistor. R1 = 97 ohms

R2 = 216 ohms R3 = 330 ohms R4 = 466 ohms

b) The Thevenin equivalent circuit will now be determined for the network to the left of the terminals a-b without disturbing the structure of the network. All the measurements will be made at the terminals a-b. Determine Eth by turning on the supply and measuring the open-circuit voltage Vab. Record the reading in Table 12.6.

Turn on the supply and adjust the potentiometer until the voltage VL is Eth/2. A condition that must exist if RL = Rth. Then turn off the supply and remove the potentiometer from the network without disturbing the position of the wiper arm. Measure the resistance between the two terminals connected to a-b and record as Rth in Table 12.6 first column. Table 12.6 Measured 6.77 V .302k ohms

Eth Rth

Calculated

c) Now we need to check our measured results against a theoretical solution. Calculate Rth and Eth for the network to the left of terminals a-b of Fig 12.8 and record in the second column of Table 12.6. Use measured resistor values. How do the calculated and measured values compare?

d) Now plot PL and VL versus RL to confirm once more that the conditions for maximum power transfer to a load are that RL = Rth and VL = Eth/2.

Table 12.7 RL 0 ohms 25 ohms 50 ohms 100 ohms 150 ohms 200 ohms 250 ohms

VL 1.27 V 2.2 V 3.2 V 4.1 V 4.7 V 5.1 V

P = VL/RL (mW)

300 ohms 350 ohms 400 ohms 450 ohms 500 ohms

5.5 V 5.7 V 5.9 V 6.1 V 6.5 V

Reviewing Graph 12.2 did maximum power transfer to the load occur when RL = Rth. What conclusion can be drawn from the results.

Does VL in graph 12.3 = Eth/2, when RL = Rth? a) Determine Rth and Eth for the network external to the 2-k ohms resistor. b) Determine the power delivered to the 2k ohms resistor using Thevenin equivalent theorem. c) Is the power determined in part b the maximum power that could be delivered to a resistor?

For the network of Fig 12.2 record the measured values of Eth and Rth from Table 12.1 in Table 12.8. then using Pspice or Multisim and methods described in the text introductory Circuit Analysis, determine each quantity and record in Table 12.8.

Table 12.8 Table 12.1 Eth Rth

Conclusion

Pspice or Multisim

In conclusion, we learned how to validate Thevenin’s theorem through experimental measurements. We became aware of the experimental procedure to determine Eth and Rth. We learned how to demonstrate that the maximum power transfer to a load is defined by the condition RL = Rth....