wwallaceLab3

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University of Guelph *

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1010

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Electrical Engineering

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Apr 3, 2024

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pdf

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3

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Lab 3 Kirchhoff’s Rule Experiment 1 Methods: The pictures to the left show the setup of the first experiment. The first image showing how the breadboard was setup in order to mimic the circuit given in the lab, with two 3.3V sources on direct opposite sides of the breadboard. There were two 2k resistors to the left of the sources, and two 1k resistors to the right of the sources. There was also a 4.7k resistor in parallel between the two sources. The second image shows the two blue alligator clips plugged into the 3.3V ports as the sources, the two white clips plugged into the ground ports, and the red clip plugged into the A7 port to record readings. Results: The image to the left is the data collected while finding the voltage across all the resistors. It can be seen that the voltage decreases from around 2.7V to 0.26V. The image to the left is the calculations used to determine the theoretical and experimental values of the currents in the circuits loops. One can see that the theoretical value of the current through the 1000 resistors is 0.000266A, the theoretical value of the current through the 2000 resistors is 0.000266A, and finally the theoretical value of the current through the 4700 is 0.000532A. Below is the diagram of the circuit that the calculations were based off.
The below chart shows the potential difference values, current calculations for each resistor and the percent difference from the theoretical values of current. Potential difference Current Current Percent Difference (%) Resistor 1 0.264V 0.000264A 0.75 Resistor 2 2.508V 0.000534A 0.38 Resistor 3 0.528V 0.000264A 0.75 Resistor 4 0.264V 0.000264A 0.75 Resistor 5 0.528V 0.000264A 0.75 Conclusion: As seen in the results section of the lab the theoretical and experiment values of the current in the resistors are almost identical, with all of the percent differences being below 1%. These findings show just how accurate kichoffs rule can be when calculating these types of values. Experiment 2 Meathods: The images to the left show the experimental setup of the second experiment. In the first image one can see how the breadboard was setup to match the diagram. In the second image one can see how the blue alligator clip is plugged into the 3.3V port and the far right white alligator clip is plugged into the DAC port which has been set to deliver 2.2V. The red alligator clip is plugged into the A7 port and used to take readings in the circuit. The last white alligator clip is plugged into the ground port. Results: The image to the left shows the different voltages through each resistor. This data was collected with the red alligator clip plugged into the A7 port. The difference in potential is around 3.3V to 0.718V.
The images to the left show the theoretical calculations for the current through the resistors in the second experiment. Using the theoretical calculations a system of linear equations was made. This SLE was made into a matrix using matlab and solved for the I values using matlab. The image below shows the RREF of the SLE matrix and the values of the currents in the system, with the top value being R1 then R2 then R3 and so on. Resistor Potetial Difference (V) Current (mA) Percent Difference (%) 1 2.547 0.5410 0.166 2 0.346 0.2161 22.3 3 0.935 0.8107 14.2 4 0.718 0.7571 5.30 5 1.065 0.5946 11.0 1. The fundemental quantity that is being conserved in the loop rule is the Voltage, as the rule itself states that the voltage in a circuit sums to zero. The quantity being conserved in the junction rule is current, as the rule itself states that the current that enters the junction is the same as the current that leaves the junction. Conclusion: The experimental and theoretical values of the current through the resistors in this circiut were almost the same. Most of the percent differences within the lab are below or within 10% of 1%. This shows the accuracy of Kirchhoffs rule when calculating the values for current, voltage and resistance.
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