Lab 3 KCL KVL

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202

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Electrical Engineering

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Apr 3, 2024

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EEE202 Experiment #3: KIRCHHOFF'S LAWS & EQUIVALENT RESISTANCE Data Sheets Name: ____Dakota Evans___________ I.D. #: ___________________ Score:_____/50 EQUIPMENT: Digital Multimeter (DMM) DC power supply Protoboard Resistors: (3) 2k , (2) 6k , and 10k Hook-up wires and leads PROCEDURES: 1. Construct the circuit shown in Figure 3.4 of the Pre-Lab, but do not connect the voltage source ; i.e., leave the connection between nodes A and B open. Use resistor values as close to those shown as possible; however, do not combine any resistors in series or parallel to form equivalent resistors closer to the requested values. Instead just use a single resistor component for each resistance specified and do not worry about slight mismatches between the desired and actual resistances. Measure each resistor value with the DMM and record in the table below. After all of the resistors have been measured and properly connected, place the DMM across the A-B nodes and measure the resistance of the entire network. This is the measured equivalent resistance. Record this resistance in the last line of the table. (The desired equivalent resistance was calculated in Pre-Lab #6.) Resistor Desired Measured % Diff. 1 2.2k 2.16k  1.81%  2 5.6k 5.56k .71% 3 2.2k 2.14k  2.73% 4 5.6k 5.55k   .89% 5 2.2k 2.17k 1.36% 6 10k 9.87k  1.3%  R AB  5.11k  5.03k  1.57 Table 3.1: Resistances in Circuit.
2. Now connect the DC power supply across the A-B nodes and use the DMM to set the voltage of the power supply to exactly 15V. (Make sure you change the DMM from reading resistance to reading voltage before turning on the power supply.)
3. Copy the voltages and currents calculated in Pre-Lab #7-8 into the appropriate “Calculated” columns in Table 3.2 below. Elemen t Voltage Current Calculated Measured % Error Calculated Measured % Error Vs   15V   15V  _ 3mA   2.94mA  2.04% 1  6V 6.43V   -6.7%  3mA  2.94mA  2.04% 2  9V  8.54V  5.39%  1.5mA  1.52mA  -1.32% 3  -3V  -3.07V -2.3%  -1.5mA  -1.42mA   5.63% 4  -6V  -5.47V 9.69%  - 1mA  -.97mA  3.09% 5  1V  .98V 2.04%   0.5mA  .44mA  13.64% 6  5V  4.48V  11.61%  0.5mA  .44mA  13.64% Table 3.2: Voltages and Currents in Circuit. 4. Measure all of the voltages specified in Figure 3.4 and record them in Table 3.2. Make sure the polarities of the measured voltages are consistent with the way they are labeled on the figure. (Some voltages should be negative.) If you have significant discrepancies between the voltages you calculated and those you are measuring, you may want to skip ahead and perform the PSpice simulation to check your theoretical values. If your measured voltages are then significantly different from the PSpice results, recheck your circuit’s wiring something must be wrong. If your measured voltages are similar to the PSpice results, but the calculated values are significantly different, recheck your math. 5. Measure all of the currents specified in Figure 3.4 and record them in Table 3.2. Make sure the polarities of the measured currents are consistent with the way they are labeled on the figure. (Some currents should be negative.) Notice that I s = I 1 , and I 6 = I 5 , therefore, only one measurement is needed for each pair of these currents. PSPICE EXERCISES: This is the first of many experiments in which you will use PSpice. It is a circuit simulation tool that allows you to determine node voltages, currents, power, frequency responses, and transient responses for a wide variety of circuits. PSpice is discussed in more detail in Appendix B. Please read Appendix B for instructions on how to use PSpice and display the results. 1. Use PSpice to layout the circuit shown in Figure 3.4, using your actual resistor values as measured in Procedure #1. Place a ground symbol at node N 3 and simulate the circuit. Figure 3.6 shows what the PSpice layout should look like before simulating, but remember to use your actual resistor values.
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Figure 3.6: PSpice Schematic. 2. Copy the voltages and currents measured in Procedure #4-5 into the appropriate “Measured” columns in Table 3.3 below. Element Voltage Current Measure d PSpice % Error Measured PSpice % Error Vs   15V 15V   2.94mA  2.99mA  -1.67% 1 6.43V  6.45V  -.3%  2.94mA  2.99mA  -1.67% 2  8.54V  8.55V   -.12%  1.52mA 1.56mA   -2.56% 3  -3.07V -3.1V   -.96% -1.42mA  -1.44mA  -1.39%  4  -5.47V  -5.45V .36%   -.97mA  -.99mA  -2.02% 5  .98V  .96V 2.08%   .44mA  .45mA  -2.22% 6  4.48V 4.49V   -.22%  .44mA .45mA   -2.22% Table 3.3: Simulated Voltages and Currents with PSpice. 3. After the circuit is simulated, select the button in the toolbar, which will show the node voltages. In Table 3.3 record the values for the voltages as they are labeled in Figure 3.4. When PSpice determines a voltage, it is always measured relative to the ground node in the circuit, which you must choose by placing a ground symbol on one of the nodes before simulating. To determine the voltage across an element not directly connected to ground, you must take the difference in the node voltages on the opposite sides of the element. For example, the voltage of V 3 can only be determined by taking the difference between the node voltages at N 2 and N 1 . To get the voltage signs consistent with the labeling in Figure 3.4, take the voltage at the ‘+’ node and subtract the voltage at the ‘ ’ node. 4. Use the mouse to select the entire circuit. Print out the schematic that shows the node voltages. (In the print window, check the box to print the selection.) Attach this printout to these datasheets.
5. Now deselect the button and select the button in the toolbar, which will remove the displayed node voltages and instead show the branch currents. In Table 3.3, record the values for the currents of I s , I 1 , I 2 , I 3 , I 4 , I 5 , and I 6 as they are labeled in Figure 3.4. To do this, you will need to pay attention to the direction of current flow. By clicking on a displayed current value in PSpice, an arrow is shown in the actual direction of current flow. When the simulation shows a current going in the opposite direction as labeled, record its value as negative. 6. Use the mouse to select the entire circuit. Print out the schematic that shows the currents. (In the print window, check the box to print the selection.) Attach this printout to these datasheets. POST-LAB QUESTIONS: 1. Calculate the percentage differences between the desired and measured resistance in Table 3.1 using the formula of:
% Diff = ( Measured Value Desired Value Desired Value ) × 100% 2. Calculate the percentage error between the calculated and measured voltages and currents in Table 3.2 using the formula of: % Error = ( Calculated Value Measured Value Measured Value ) × 100% Note: the main reason for the error in the calculations is that the calculated quantities were based on the exact resistor values shown on the circuit in Figure 3.4 and not the actual resistor values used. 3. Calculate the percentage error between the measured and simulated voltages and currents in Table 3.3 using the formula of: % Error = ( Measured Value Simulated Value Simulated Value ) × 100% Note: since the PSpice simulations were based on the actual resistor values used, the percentage error in the measured quantities should be very small.
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4. Substitute the measured currents in Procedure #5 into the 3 KCL equations derived in Pre-Lab #1-2, and verify that the sum of the currents at any node is zero (to within the tolerance of your measurements). 5. Substitute the measured voltages in Procedure #4 into the 6 KVL equations derived in Pre-Lab #4, and verify that the sum of the voltages around any loop is zero (to within the tolerance of your measurements).