ANALYSIS OF A DC CIRCUIT PROBLEM 5Objective: Analyze the following DC circuit using mesh analysis and Thevenin's theorem. Determine the unknown voltage, current, and direction of flow through the circuit. Evaluate the advantages and disadvantages of meshing and Thévenin's theorem. Assumptions: In the above circuit, the current (I1, I2, I3) is assumed to flow in the conventional direction, i.e. clockwise. The source voltage indicated by XX was assumed to be 86 V. Mesh Analysis Mesh analysis is a method used to solve planar circuits for voltage and currents at any location in the circuit. Mesh analysis uses Kirchhoff's voltage (and current) laws to understand and solve these planar circuits. Mesh analysis is a systematic approach to solving planar circuits and reduces the number of equations needed to solve the circuit for all voltages and currents. Similar methods exist, such as the branch current method which is similar in style using Kirchhoff's and Ohm's laws. In this case, the circuit will be analyzed using standardized mesh analysis using Kirchhoff's voltage law. Figure 1 below shows the (estimated) loop directions and the current and voltage analysis points are surrounded by a sun shape. Figure 1 Labeled circuit with loop directions estimated using Kirchhoff Voltage Law (KVL) Loop 10 = -86 + I_1 R_25+R_10 (I_1-I_2)0=-86+25I_1+10(I_1- I_2)86=35I_1-10I_2Loop 20=R_10 (I_2-I_1)+R_40 (I_2-I_3)+R_20 (I_2-I_4)0= 10(I_2-I_1)+40(I_2-I_3)+20(I_2-2.5 )50=-10I_1+70I_2-40I_3Loop 30=R_30 I_3-40+R_40 (I_3-I_2)0=30I_3-40+40(I_3 -I_2)40=-40I_2+70I_3By converting the above equations to matrix format, we get[(35&-10&0@-10&70&-40@0&-40&70)][(I_1@I_2@I_3 )... middle of paper ......must be searched. Comparative mesh analysis will allow more detail to come out of the analysis if it does not face similar restrictions (planar circuits); Table 3 (above) shows that the Thevenin analysis does not allow the measurement of current in certain parts of the network. When analyzing a circuit whose potential current (although all or part of the network) is too high, Thevenin analysis should not be used for the above reasons. If the circuit does not exhibit significant current changes, the ease of calculation with Thevenin's method would make this style preferable. In conclusion, engineers prefer to choose one calculation technique over another, although there are some minor differences in the final output of the functions. The examples throughout this document highlight the advantages of mesh analysis over Thevenin analysis..