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13 Nov 2019
(3) A transformer is built from two types of wire, #1 and #2, with cross sections q1 and q2 respectively. The #1 wire is wound onto the primary coil of the transformer with n! turns, while the #2 wire is wound onto the secondary coil with n2 turns. The current in the primary coil is i1, and the current in the secondary coil is i2. Electrical engineers have found that the heat produced by electrical current in the coils can be minimized by minimizing the function 91 42 where the resistivity Ï and the diameters D1 and D2 of the iron cores are constants. (a) From transformer theory, it turns out nii] - n2i2 - constant. By an argument involving insulation thickness, one can show that q1 = azh/ni and g2 :nyh/n2, where a and h are constants. Use these relations to simplify the expression for C (b) Physical constraints give x + y (D2-D1). Apply the method of Lagrange multipliers to find x and y which minimize C subject to this condition.
(3) A transformer is built from two types of wire, #1 and #2, with cross sections q1 and q2 respectively. The #1 wire is wound onto the primary coil of the transformer with n! turns, while the #2 wire is wound onto the secondary coil with n2 turns. The current in the primary coil is i1, and the current in the secondary coil is i2. Electrical engineers have found that the heat produced by electrical current in the coils can be minimized by minimizing the function 91 42 where the resistivity Ï and the diameters D1 and D2 of the iron cores are constants. (a) From transformer theory, it turns out nii] - n2i2 - constant. By an argument involving insulation thickness, one can show that q1 = azh/ni and g2 :nyh/n2, where a and h are constants. Use these relations to simplify the expression for C (b) Physical constraints give x + y (D2-D1). Apply the method of Lagrange multipliers to find x and y which minimize C subject to this condition.
Lelia LubowitzLv2
28 Apr 2019