Hw7-Solution - Assignment 7 FS 2007 ECE 430 Text 4.8 a...

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Assignment 7 FS 2007 ECE 430 Text 4.8 a) First find the coenergy. It is magnetically linear, so we can simply sum up the 1/2*Lpq*ip*iq terms: To get the torque, just take the derivative with respect to theta: b) We are not given the angle, so the torque will depend on theta. Plug in the values for i1 and i2: c) We need to find the maximum of this function. Brute force differentiation and solution is difficult since it is transcendental. It is easier to plot it and inspect. From inspection: Te (max) = 0.002735 N-m Theta(max) = 310.5 deg (= -45 deg)
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text 4.9 Once again, this is a magnetic linear system. Simply sum up the 1/2 Lpq*ip*iq to get the answer for coenergy: then differentiate with respect to theta: Text 4.12 If the field energy is: Then the force is negative derivative of this with respect to x However, we are given that the current is held constant, so we really need an expression in terms of current, since the flux linkage may not remain constant as x is changed. The current is given by
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