Fall2010_HW4_sol - ECE 430 HW#4 Solutions Fall 2010 Problem...

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ECE 430 HW #4 Solutions Fall 2010 Problem 3.2 (a) By defining the dot on the upper portion of the left coil, Figure 1 is able to show the appro- priate dot location for the right coil. If current were to flow into the dot on the right coil the resulting flux would flow in the same direction (clockwise) as the flux resulting from the ex- citation into the dot of the left coil. Since the directions of the flux paths match, the location of the dot markings are correct. Figure 1: Dot Markings - Problem 3.2 Figure 2: Magnetic Circuit - Problem 3.2 (b) Using the magnetic circuit in figure 2, the flux linkages can be determined by applying mesh analysis on the system: φ 3 = φ 1 + φ 2 N 1 i 1 = φ 1 R 1 + R 3 ( φ 1 + φ 2 ) N 2 i 2 = φ 2 R 2 + R 3 ( φ 1 + φ 2 ) Solving this system of equations with Mathematica: In[71]:= R1=2*10ˆ6; R2=2*10ˆ6; R3=3*10ˆ6; N1=100; N2=50; sol=Solve[{N1*i1==\[Phi]1*R1+R3*(\[Phi]1+\[Phi]2),N2*i2== \[Phi]2*R2+R3*(\[Phi]1+\[Phi]2)},{\[Phi]1,\[Phi]2}]; \[Lambda]1=N[N1*\[Phi]1/.sol] \[Lambda]2=N[N2*\[Phi]2/.sol] Out[77]= {0.0003125 (10. i1-3. i2)} Out[78]= {0.00015625 (-6. i1+5. i2)} This code results in the answer of: 1
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