10-6-11 Nodal and Mesh Analysis

# Figure 1 the circuit given for part i with the

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Figure 1. The circuit given for part I, with the Multisim probes shown; note the direction of each. With this simulation, we were able to find the voltages at each of the required points. Comparison between these values and the measured values are in Tables 1 and 2. Table 1 concerns voltage at each of the points, while Table 2 has the currents delivered by each power supply. Table 1. The Mutisim voltages for this procedure Point Multisim Voltage () Measured Voltage () Percent Difference A 3.10 3.06 1.31% B 2.91 2.87 1.40% C 3.78 3.74 1.07% Table 2. The Mutisim currents for this procedure From Source Multisim Current () Measured Current () Percent Difference 2.15 2.2 2.27% 0.622 0.64 2.81% Next, we calculated the voltages at each of the points by hand, using nodal analysis. This is shown below. Each of the currents assumed to be flowing into the point are on the left side of the equal sign, while the currents assumed to be flowing out are on the right side. These equations, assuming , , and each of the values are known, simplify down into the following.

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Finally, all of these equations can be plugged into a matrix and solved. Table 3. The calculated voltages for this procedure Point Calculated Voltage () Measured Voltage () Percent Difference A 3.10 3.06 1.31% B 2.91 2.87 1.40% C 3.77 3.74 0.80% Once the voltages of the points were calculated, it was trivial to find the currents being output by the voltage sources. Simply solving Kirchhoff’s Current Law, using the above equations, is enough to find the currents. Table 4. The calculated currents for this procedure From Source Multisim Current () Measured Current () Percent Difference 2.15 2.2 2.27% 0.623 0.64 2.66% Question 1. How much power did the whole circuit consume? Demonstrate how you calculated it.
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