Question

126 S. Consider the large circuit shown in Figure 3, where the components have the following values: We will use Kirchhoff's rules to calculate the current passing through each of the nineteen circuit components. ineteen components in this circuit, there are only twelve through two components that are in series. After considering this fact, draw twelve arrows on Figure 3, indicating twelve distinct currents. Label these currents as 112 These twelve currents are unknown, and we wish to find their distinct currents. This is because the same current passes values [Continued on Next Page 127 s.2. Using Kirchhoffs rules, write twelve equations for the circuit in Figure 3. Your equations must be linearly independent. There are six obvious loops that you can choose. Only five of these loops will give you "distinct" equations. There are also eight obvious junctions that you can choose. Only seven of these junctions will give you distinct equations. When working with large circuits like this one you should carefully organize you work, and have a teammate check it for you. Using both the voltage rule and the 2 . current rule, write twelve distinct equations below 7 Flgure 3 128 .3 Write your twelve equations as a matrix equation. Then enter the matrix equation into Excel, and solve for the currents 1zRound your solutions to four decimal places and record them below Are any of the currents that you calculated negative? If so, what does this mean? 5.4. Let's check your work so far by verifying a couple of things. 5.4.1. Multiply your matrix by its inverse, and verify that the product is the identity matrix. 5.4.2. Look at each of the four junctions in Figure 3, and verify that the currents at that junction add up to zero. 5.5. Once you have calculated the currents, you should be able to calculate any voltage in the circuit. Calculate the following voltages All of the circuits we have analyzed so far have involved only batteries and resistors 6. Why or why not? 7. In step 2, you solved for the unknowns x, y, and z in Eq. 9. After entering matrices A and b, you calculated the inverse matrix A-1. Then, you multiplied A-1 and b to find the unknowns. Can you make this process more efficient by using a single "nested" Excel command? Write this command exactly as you would type it into Excel:

Answer 1

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