Question

Problem 2: Total Impedance (25 Points) n electric circuit consists of two components as shown in the figure below. The values of the impedance of the two components are Zi-Ri + M and Z2-R2-JXc, wh XL 100 Ω, R2-50 Ω, and Xc-125 Ω. 21 and Z2 as complex numbers in both their rectangular and polar forms. mine the complex conjugate of Z2 and compute the product of Z222 a) Write Z1Z2 Compute the total impedance of the two components- result in both rectangular and polar forms. 122 and express the a c) 2+ Z1+22

Answer 1

Z_1 = 75 + j 100, Z_2 = 50 - j 125 rectangular form Z_1 = squareroot 75^2 + 100^2 angle tan^-1 (100/75) Z_1 = 125 angle 53.13 Z_1 = 125 e^j 53.13 degree polar form Z_2 = squareroot 50^2 + 125^2 angle tan^-1 (-125/50) Z_2 = 134.63 angle -68.2 degree Z_2 = 134.63 e^-j 68.2 degree polar form (b) Z_2 * = 50 + j 125 Z_2 Z_2* = (50 - j 125) (50 + j 125) Z_2 Z_2* = 50^2 + 125^2 = 18125 \r\n (c) Z = Z_1 Z_2/Z_1 Z_2 = (75 + j 100) (50 - j 125)/75 + j 100 + 50 - j 125 Z = 16250 - j 4375/125 - j 25 Z = [16250 - j 4375]/125 - j 25 [125 + j 25]/[125 + j 25] = 2140625 - j 140625/16250 Z = 131.7307 - j 8.654 rightarrow rectangular form Z = squareroot 131.7307^2 + 8.654^2 angle tan^-1