Problem 1. (25 pts) For this problem, consider a right-hand…
Problem 1. (25 pts) For this problem, consider a right-hand coordinate system wherein the x-axis is directed to the right on your paper, the y-axis is directed toward the top of your paper, and the z-axis is pointing out of your paper. A winding with 10 turns is wound around the rectangle with corners (x,y,z) = (-1,-2,0), (2, -2, 0), (2, -2, 3), and (-1, -2, 3). The winding is wound such that the direction for positive flux is in the same direction as the positive y-axis. Now suppose that within the rectangle B=(1+2x2yz)aysin(200t)T{“version”:”1.1″,”math”:”B=(1+2x2yz)aysin(200t)T”} where ay{“version”:”1.1″,”math”:”ay”} is the unit vector is the y direction, and t represents time. The winding (coil) is open circuited. Using the definition of flux, flux linkage, and Faraday’s law determine an expression for the voltage (as a function of time) that would be measured across the coil, assuming the usual passive sign convention we used in class. The answer should be of the form v=57sin(100t+π/4){“version”:”1.1″,”math”:”v=57sin(100t+π/4)”} (which is incorrect, but you get the idea). Problem 2. (25 pts) Consider the EI core device below. Derive an expression for the absolute value of electromagnetic force on the I-core in terms of N, i, ds, ws, w=wb=we=wi=wc/2, g, μr{“version”:”1.1″,”math”:”μr”}, and the permeability of free space μ0{“version”:”1.1″,”math”:”μ0″}. Problem 3. (25 pts) Consider the transformer T-equivalent circuit (referred to the primary). The primary to secondary turns ratio is 10. Given the primary voltage and that the radian frequency is ωe{“version”:”1.1″,”math”:”ωe”}, we want to find the actual secondary voltage. (a) 6 pts. If the physical resistance of 2.5 Ohms is placed on the secondary, what value of resistance do I use when performing calculations on the equivalent circuit? (b) 6 pts. Write an expression for Zb as we used it in class (see below). Use symbols when you don’t have numerical data. Something like Zb=3r1+jωeLl1+jωeLm4jωeLm+4{“version”:”1.1″,”math”:”Zb=3r1+jωeLl1+jωeLm4jωeLm+4″} (which is incorrect). (c) 7 pts. Suppose the phasor representing the magnetizing voltage is denoted v~m{“version”:”1.1″,”math”:”v~m”} and the radian frequency is ωe{“version”:”1.1″,”math”:”ωe”}. Derive an expression for the phasor representing the referred secondary voltage in terms of v~m{“version”:”1.1″,”math”:”v~m”}, ωe{“version”:”1.1″,”math”:”ωe”}, and the equivalent circuit parameters (using symbols where you don’t have numerical values as in part (b)). (d) 6 pts. Suppose v~2’=60∠30°{“version”:”1.1″,”math”:”v~2’=60∠30°”}. Write a corresponding expression for the secondary voltage in the time domain as we would measure it with an oscilloscope. Here your answer should look like v2=257cos(ωet+5π180){“version”:”1.1″,”math”:”v2=257cos(ωet+5π180)”}, which is wrong but again you get the idea. Problem 4. (25 pts) Consider the following flux linkage equations. Determine the following: (a) {5 pts} if the system is magnetically linear (b) {15 pts} the field-energy (c) {5 pts} electromagnetic force in terms of x{“version”:”1.1″,”math”:”x”}, λ1{“version”:”1.1″,”math”:”λ1″}, and λ2{“version”:”1.1″,”math”:”λ2″}. Also note that the system is conservative, so you won’t need to verify this. i1=λ1+6(λ1+3λ2)3(2+x)i2=3λ2+18(λ1+3λ2)3(2+x){“version”:”1.1″,”math”:” i1=λ1+6(λ1+3λ2)3(2+x)i2=3λ2+18(λ1+3λ2)3(2+x)”} Congratulations, you are almost done with Exam 1. DO NOT end the Honorlock session until you have submitted your work to Brightspace. When you have answered all questions: Use your smartphone or scanner to scan your answer sheet, and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Submit your exam to this assignment: Exam 1 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.