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exam1[1] - (25 1 Consider the square-core inductor Neglect...

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1. Consider the square-core inductor. Neglect leakage. Provide numerical answers and indicate units in- side [ ] - use scientific notation for large/small numbers (e.g. ). Must show work for credit. 2. Neglect resistances. 3 10 6 × 2 cm 2 cm 12 cm 3 0 10 H/m r μ μ - = 2 A 20 Turns l 1 l 2 10 m = = + - + - A A V 1 t ( ) 2 44 20 t ( ) cos V = X m 1 _______ Ω = X l 1 _______ Ω = I ˜ 1 __________ = I 1 t ( ) 2_____ ____ t ____ ° + ( ) cos = m 10 5 H 1 = N 1 100 = N 2 200 = v 1 i 1 v 2 (20) (25) H ____________[ ] = B ____________[ ] = Φ ____________[ ] = λ ____________[ ] = L inductance ( ) ____________[ ] = [O i] [O i]
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3. 4. 1’ 1 2 2’ θ r L 11 L 22 L 12 max , 5 mH = = = T e (a) Superimpose and label the magnetic axes for the 1- and 2-windings on the figure to the left. (b) mH (c) If , sketch the locations of , , and on figure to left. (circle one) , (d) If and , V L 21 θ r ( ) ____ _____ ____ θ r ____ ° + ( ) cos + = i 1 i 2 1A = = N s S s N r S r T e 0 > T e 0 < i 1 i 2 1A = = θ r 60 t = V 1 t ( ) _______ ______ t ______ ° + ( ) cos = 1’ 1 θ r , (a) mH (b) If and the load torque is zero, sketch (in space be- low the figure to left) the cross sectional view at the stable equi-
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