Group Projects and Practice Problems using the Phasor Domain

Objective:
The new method of transforming the circuit to the phasor domain but now applying all the methods we covered this semester such as nodal analysis, mesh analysis, etc. During calculations, we will be required to create a matrix of complex numbers in order to solve for unknown current or voltages. Though, we must used rref in order to solve for the unknowns when using MATLAB. Superposition are important to solve for a circuit where there are two sources with different angular frequencies being applied. We covered source transformations using the phasor domain. We reflect back to source transformation which is, when a resistor is in parallel with a current source, we can replace it with a voltage source. Also, we can replace a voltage sources which is in series with a resistor with a current source in parallel with the resistor used to calculate the current source.

Group Practice:
 1. The problem below shows a circuit in which there is a current source and are told to find the current through the .1F capacitor. The first step is to find the phasor domains for the inductor and capacitor as shown in figure 1. We can then apply nodal analysis at node one solve simplify into a linear equation. We then apply nodal analysis to the second node and simplify in terms of a linear equation. Since, we are able to solve for voltage 2 in terms of voltage 1. We can use substitution in this case or place it into a matrix and solve in MATLAB. After the voltage is solved we can change it to polar form and solve for the current.

Figure 1. Finding the current through the capacitor.

2. The following problem tells us to find the currents using KVL using 3 loops. However, we notice that one loop is given to us. We apply KVL and place it into system of linear equation and place it into a matrix for MATLAB to solve. It is important to first transform the circuit to its phasor domain before starting to work on it.

Figure 2. Solving for the current using 

3.  The problem below requires us to find the thevenin equivalent from terminals a and b. The first step is to transform the circuit into the phasor domain. We will apply KCL at node 1 and then KVL to the right loop as seen in figure 3. 

Figure 3.

Learning Outcome:
There was no Lab today but we practice using KVL,KCL, mesh analysis, nodal, analysis, thevenin equivalent in the form of a phasor domain. Same process is implemented when dealing with the phasor domain. We also covered the grading rubric and what is expected for the final project presentation. We got together with out partners and created a plan for the upcoming days. There is a pert chart that we must complete and include in our presentation.