MAC 2210

MAC 2210 Complex Numbers Homework 1. Imaginary numbers have many applications in the study of electrical circuits, especially those called alternating current circuits or AC circuits. Briefly, the components of an AC circuit are (i) current I (measured in amperes), (ii) voltage V (in volts), and (iii) the impedance Z (measured in ohms). The impedance of an electrical circuit is a measure of the total opposition to the flow of current through the circuit and is calculates as Z = R+iXL -iXc where R represents a pure resistance, Xc represents the capacitance, and Xz represents the inductance. Each of these is also measured in ohms (symbolized by $2 ). (a) Find the impedance Z if R = 10 02, XL = 7 0, and Xc = 13.3 0. (b) The voltage V across any element in an AC circuit is calculated as a product of the current / and the Impedance Z. That is, V = IZ, which is known as Ohm's Law. Find the voltage in a circuit with a current I = 5 - 2i amperes and an impedance of Z = 6 + 21 0. (c) In an AC circuit, the total impedance (in ohms) is given by 2 = 7 + 7, where Z represents the total impedance of a circuit that has resistors Z1 and Z2 wired in parallel. Find the total impedance Z if Z1 = 3- i and Z2 = 2 + 1