EECE 210 Exam 2, Fall 2004

AMERICAN UNIVERSITY OF BEIRUT Department of Electrical and Computer Engineering EECE210 Fall 2004 Quiz 2, December 15, 2004 Prof Karameh Directions: - NO PROGRAMMABLE CALCULATORS ARE ALLOWED. - You will have 1.5 hrs for this quiz. - Write down your initials in ink on all the pages. DO IT NOW! - Answers must be explained or derived. DO NOT just write down an answer. - It is a good idea to read the whole test before you begin. Some problems are divided into several parts with percentages indicated. You might be able to solve different parts independently. - DO NOT talk to any of your colleagues under any circumstances. You will be penalized without warning. YOUR NAME HERE: EECE210 - Quiz 2- Fall 2004. NAME: PROBLEM 1 (15%) Consider the network shown in figure 1. The Switch was at the 20 Ω for a long time for t < 0. At t=0, switch is moved to the 10 Ω resistor. (a) (12 %) Find the current in the inductor iL(t), t ≥ 0. (b) (3 %) Find the maximum energy stored in the inductor. − i (t) L . 20 Ω Ω Ω Ω 0.1 H 2.5 5 100 V + t=0 . . . 15 Figure 1: Problem 1 PROBLEM 2 (12%) Consider the network shown in figure 2. Find the values of resistors R1, R3 so that the current supplied by the voltage source Vs is zero for all time. All op-amps are ideal. R1 Ω K Ω K Ω K Ω K Ω K Ω K Vs R3 . _ + + _ 40 10 5 10 15 30 + _ . . . . . . . Figure 2: Problem 2 EECE210 - Quiz 2- Fall 2004. NAME: PROBLEM 3 (18%) Consider the network shown in figure 3. (a) (4%) Write the differential equations necessary to compute the voltage in the resistor R for any source voltage v(t). (b) (4%) If v(t) = 12 − 201e−t, which, if any, of the following currents might actually have came from the circuit? (1) i1(t) = 0.24 − 2e−t, i2(t) = 4e−t. (2) i1(t) = 0.12 − 4e−t, i2(t) = 3e−t. (3) i1(t) = 0.24 − 4e−t, i2(t) = 3e−t. (c) (10%) Find the Thevenin equivalent circuit for the network to the left of terminals a,b of the resistor. (v(t) = 100cos100t volts). − . . . + 50 Ω 2 H 5 H 3 H 100 cos(100t) V a b v(t)= . . R=1Ω i (t) i (t) 2 1 Figure 3: Problem 3 Problem 4 (15%) Find the output voltages v1 and v2 of the ideal op-amps shown in figure 4. Ω K Ω K Ω K Ω K Ω K 2 v v1 Ω K . +_ _+ . . . . . + + 8 V 12 V 2 2 4 1 2 0.2 Figure 4: Problem 4 EECE210 - Quiz 2- Fall 2004. NAME: PROBLEM 5 (20%) For the network shown in figure 5, find the current i2(t). Show all your work. i (t) 2 . Ω Ω 1Ω 1 0.67 I1 I1 1 1Ω 5sin2t + + 1 Amps volts . . . . . 1 H 1 F Figure 5: Problem 5 PROBLEM 6 (20%) Consider the circuit shown in figure 6 below. The switch was open for a very long time t < 0. At t=0, switch is closed. (a) (12 %) Given: L=5 H, C=4 F, R1 = 3Ω, and R2 = 2Ω. Find the voltage in the capacitor vc(t) for t ≥ 0. (b) (3 %) Is the circuit response you obtained in part (a) underdamped, critically damped, or overdamped? explain. (c) (5 %) If L= 5 H, C=4 F, find R1, R2 such that the circuit response is critically damped. − vc − R . + 1 R2 L C t=0 6 V + . . Figure 6: Problem 6