EE1111 Lab Manual-Diploma - Lab 4

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Diploma Program Course EE1111 EE1111 – Electrical and Telecommunications Engineering Student Name: …………………… Student ID: ………………………… Online LABORATORY No. 4 Worksheet

Contents Lab Experiment 4: Circuit theorems ...................................................................... 1 Aims of this experiment ............................................................................................................ 1 Videos and guides for review .................................................................................................... 1 Lab 4: Part A. Pre-Lab Work ...................................................................................................... 2 Lab 4: Part B. Hardware Explanation ........................................................................................ 2 Lab 4: Part C. Simulation and Discussion .................................................................................. 5 Required components ............................................................................................................ 5 I. Thevenin’s theorem ........................................................................................................ 5 II. Norton’s theorem ......................................................................................................... 7 III. Superposition theorem ................................................................................................. 7 IV. Maximum power transfer ............................................................................................. 8

Lab Experiment 4: Circuit theorems Aims of this experiment The aim of this lab experiment is to investigate the following circuit theorems: 1 Thevenin’s theorem. 1 Norton’s theorem. 2 Superposition. 3 Maximum power transfer theorem. Videos and guides for review List of suggested videos : Power supply Multimeter List of suggested guides from Appendix in the Online Laboratory Guide:  DC power supply  Digital multimeter Page 1

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Lab 4: Part A. Pre-Lab Work Make sure you complete the online quiz for Lab 4 before attending your session. Note that this quiz can be found in Moodle in the Laboratory section. Lab 4: Part B. Hardware Explanation Please complete all the tasks given in this section during the lab session. Do not forget to watch the related lab videos and guides that are suggested for this lab experiment. 1. Annotate the diagram in Figure 4 .2, on the next page, to show how you would set up the circuit in Figure 4 .1 if you were in the lab. Assume that we wish to measure the DC current through R 6 for this experiment. You may copy the image in Figure 4 .2 into MS Paint, add your annotations, and then copy the annotated image back into this document. Refer to the Preface section in the Online Lab Manual for an example annotated image. The annotation in Figure 4 .2 must show:  The components on the picture of the breadboard (in a dark blue colour)  Connections on the picture of the breadboard in red or black (or any other relevant colour) depending on the colour of the cable or wire insulation that you would use in a lab.  The cable connections between each piece of equipment and the breadboard and/or the components on the breadboard. Also, be prepared to explain to the lab demonstrator what connection type you would use at each end of the cable (i.e. banana plug, BNC, alligator clamp, etc.). It may be helpful to add text descriptions of this to your diagram. Figure 4.1: Resistive circuit for Lab Experiment 4. Some helpful tips with this exercise are:  Ensure that annotated lines are thick enough to be easily seen, but not too thick that it becomes difficult to see what breadboard holes you are connecting wires to.  Ensure that you understand why you have connected equipment in the particular configuration as lab demonstrators may ask you this question.

Figure 4.2: Part B. Equipment diagram for annotation exercise. Page 3

2. Explain how you would set up the DC power supply and multimeter in the following Answer Box. Include equations to prove that you have checked that the estimated current flowing through R 6 does not exceed the rating of the multimeter. These are important checks that you should do whenever you connect a multimeter to a circuit. Also, include equations to estimate what the current draw from the dc power supply should be. From this calculation, explain what voltage and current settings you would program the dc power supply with. Make sure you watch the Lab Guidance video explaining the dc power supply to understand what these settings mean. For the dc power supply, include explanations on how you would set up:  Channel 1, 2 and 3 voltage and current settings (if a channel is not used, just say zero for this channel)  The series/parallel buttons in the dc power supply (explain why this setting is important or not important for your experimental setup)  The Power button and ON/OFF button (what pressing these buttons do and when they should be pressed) For the multimeter, include an explanation on how you would set up:  Current measurement (What buttons are required? Should you press the DCV, ACV, Ω, DCA, ACA or the DC+AC button and why?)  How would you set the scale of the current measurement? 1.According to experiment’s requirement to set like in 10V. and max current limit to 2A (due to our multimeter can accept max 2A) 2.The mode of power supply should be independent mode. In this experiment, we just need using one chancel. 3. The function of the power button and the switch button is to provide power and press it to ensure the circuit is correct and safe. 4.Current measurement needs to press DCA, because it is a DC circuit and we want measure current. 5.Start with the smallest measurement. If there is a reading, then there is no need to change the scale. If it shows 1, then change to a larger measurement scale. Page 4

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Lab 4: Part C. Simulation and Discussion For this section, you will use Autodesk Circuits in TinkerCAD to build and test the circuits for each question. IMPORTANT : For each Answer Box, show pictures of the circuit that you have used in Circuits in TinkerCAD. Make sure that you include the multimeter readout in the picture when finding the voltage and current. Required components In this experiment you will be required to use the following components:  A breadboard.  100 Ω , 220 Ω , 330 Ω , 470 Ω , 680 Ω , 1 kΩ , and 1.5 kΩ resistors. I. Thevenin’s theorem 1 Build the circuit of Figure 4 .3 on your breadboard in Circuits in TinkerCAD. Consider R 6 to be the load resistor. Measure the voltage across R 6 and the current through it ( V L and I L ), and calculate the power consumed ( P L ). Figure 4.3: Resistive circuit for Lab Experiment 4. V_L = 2.81V I_L = 1.87mA P = V_L * I_L = 0.00525W 1 Now remove R 6 from the terminals c and d (the terminals clearly become an open circuit). Measure the open circuit voltage across terminals c and d . What does this voltage represent? V_L = 3.68V is the thevenin voltage. 2 Explain why the simulated voltages and currents will differ from practically measured voltages and currents for the circuit shown in Figure 4 .3. Think about the practical limitations of resistors, dc power supplies and multimeters. (Tolerances, measurement resolution, etc.)

The wires have resistance and the power supply have inter resistance, measure errors. So there are different. 3 Measure the Thevenin resistance R Th by appropriately disabling all independent sources in your circuit. Explain why the simulated Thevenin resistance will differ from the practical Thevenin resistance. Explain how you would measure Thevenin resistance in a practical circuit. R Th = 465ohms The wires have resistance and the power supply have inter resistance, measure errors. 4 Build the Thevenin equivalent circuit on your breadboard and connect it to the load resistance R 6 . Measure the voltage across the load and compare it to the voltage you measured in question 1 . Are they similar? Would they be similar in a practical lab environment? I_L = 1.83mA; V_L = 2.75V; Yes Yes II. Norton’s theorem 5 Consider the same circuit as in Figure 4 .3. Measure I N as the short-circuit current between terminals c and d (where R 6 was connected). How would the simulation short- circuit current that you have determined be different from the practical short-circuit current? (Hint: Think about any stray resistances that might not be present in your simulation but occur in practical circuits) I N = 7.91mA The wires have resistance and the power supply have inter resistance 6 Calculate I N = V Th R Th and compare it to the measured value obtained in the previous question.

I N = V Th R Th = 3.68/465 = 0.00791A is same III. Superposition theorem 7 Build the circuit of Figure 4 .4 on your breadboard. Set V s 1 and V s 2 to be 10 V and 15 V , respectively. Then, measure the currents I 1 , I 2 , and I 3 with the given directions. I1 = 4.31mA I2 = -24.7mA I3 = 29mA Figure 4.4: Resistive circuit to verify the superposition theorem. 8 Disable V s 1 and measure the same currents but label them as I 1 ' , I 2 ' , and I 3 ' . I1 = -38.8mA I2 = -50.8mA I3 = 11.8mA 9 Disable V s 2 and measure the same currents but label them as I 1 ' ' , I 2 ' ' , and I 3 ' ' . I1 = 43.1 mA I2 = 25.9 mA I3 = 17.2 mA 10 Confirm the principle of superposition using your previous measurements. I1 = 43.1 + ( -38.8 ) = 4.3 mA I2 = 25.9 + ( -50.5 ) = -24.6 mA I3 = 17.2 + 11.8 = 29 mA

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IV. Maximum power transfer 11 Build the resistive circuit shown in Figure 4 .5 on your breadboard. Measure the voltage across R L ( V L ) and the current flowing through it ( I L ), and then calculate the power consumed ( P L ) for the different values of R L given in the table below. Write down all your measurements and calculations in the Table. Figure 4.5: Resistive circuit to examine maximum power transfer theorem. Load resistor R L Load voltage V L Load current I L Load power P L 100 Ω 1.77V 17.5mA 0.03078W 220 Ω 3.20V 14.5mA 0.04621W 470 Ω 5.01V 10.6mA 0.05320W Ω 5.92V 8.69mA 0.05142W 6.80V 6.80mA 0.04528W 12 Plot the variation of the load power P L with respect to the variation of the load resistor R L using the collected data. Please use Excel to perform this plot function and copy the graph into this document. Think about whether resistance or power should be on the x -axis. Identify at what point the power is maximum. Calculate the theoretical value of the maximum power transferred for the circuit of Figure 4.6. Will the load resistance value which gives the practical maximum power transfer be similar to the simulated/theoretical maximum power transfer load resistance? What will cause any discrepancy between the simulated and practical values? The power supply has internal resistance. In circuit transmission, there will be energy loss. Ammeter and voltmeter also have internal resistance. In the calculation, the existence of significant figures will also cause differences. Therefore, there will be a certain calculation error between the simulated value and the actual value.