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Unformatted text preview: 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]\[Lambda]2=N[N2*\[Phi]2/....
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This note was uploaded on 10/05/2010 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Electromagnet

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