Download Phasor Circuit Solutions & Impedance Calculation in EE Homework - Prof. Romel Del Rosario and more Study Guides, Projects, Research Electrical and Electronics Engineering in PDF only on Docsity! ENEE 204 Fall 2008 HW #4 Due: in class Thursday, Oct. 2, 2008 Prof. Gomez Problem 1. M&L, 3.13, A simple circuit using phasor analysis Problem 2. M&L, 3.20. Practicing KCL, KVL using phasors. Consider the circuit in Figure P3-20(a) and Figure P3-20(b) on page 93 of the text. a. Write down the impedance of each branch, noting that in some of the elements in (a) have been combined into single branches. b. Use the reference directions indicated in the figure. Use KVL, KCL and write down the matrix equations to solve for I1-I6, assuming that Vs (source voltage) is known. c. Let Vs=170sin(377t), R1=R2=R3=10Ω, C1=100 µF, C2=200 µF, C3=300 µF, L= 27 mH. Substitute the values into the matrix equation in b) and solve for the currents in PHASOR representation. Use calculator. Problem 3. Successive simplification of complex impedance. Again consider the circuit Figure P3-20 on page 93 of the text. a. Using the process of successive simplification, i.e., combing the elements that are in series and in parallel, find an expression I5, the phasor current for branch 5 in the circuit. Express result in terms of the impedances Z1, Z2, etc. on each branch. For simplicity, just use the symbol ‘//’ to indicate that the effective impedance is parallel, e.g. Zk//Zl = Zk Zl /( Zk + Zl) for elements Zk and Zl. Similarly, use the ‘+’ symbol to indicate that the effective impedance for Zk and Zl in series is Zk+Zl. Write down the phasor forms of the sources. b. Use the values in Problem 2c, and solve for all the currents (in phasor form). c. Express phasor currents in time-domain form. Problem 4. Calculating the effective impedance of a complicated network. Assume all units are in Ohms. Find the effective impedance ZAB between the nodes A and B. Hint: The impedance ZAB is just the phasor voltage divided by the phasor current. Be clever. Problem 5. Learning how to simplify AC circuits. Also, understanding average power and power factor. For the circuit given below, Vs(t) = 100sin(300πt - 3π/4) V. a. Use phasors to solve for the voltage across R. Recognize that some elements in parallel and simplify them. Convert the phasor to time dependent voltage. b. What is the average power dissipated in the inductor, resistor and capacitor, respectively? c. What is the power factor of the entire impedance network? Problem 7. Consider the circuit. a. Find the value of the frequency (in Hertz) such that Io(t) is in phase with V1. b. Find the steady state current, Io(t) in time domain.
