ECE212_2008_FinalExam.pdf

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Department
Electrical & Computer Engineering
Course
ECE385H1
Professor
Micah Stickel
Semester
Winter

Description
ECE 212 H1F Pg 1 of 12 ECE 212 - Circuit Theory Final Examination December 5, 2008 1. Policy: closed book, calculators allowed. Show all work. 2. Work in the provided space. 3. The exam has 3 problems and 12 pages, including the cover page and extra sheet. Name:___________________________________________ Student Number: __________________________________ Problem 1 [33 pts] Problem 2 [33 pts] Problem 3 [34 pts] Total [100 pts]: Problem 1 [33 marks] In the circuit below, the switch has been closed for a long time. At t=0, the switch moves from closed to open position R t = 0 S R C _ + v (t) iL(t) C + L 12 V _ (a) [5 points] Derive a differential eqLation for i (t) for t>0. (5 marks) (b)[2 points] Find the circuit characteristic equation for t>0. (2 marks) (c)[5 points] For R = 8 Ω, R =S2 Ω, C = 50 mF and L = 200 mH, determine the initial conditions for iL(t) and vC(t) at t = 0. (d) [4 points] For the given parameters in (c), determine the final conditions for i (tL and vC(t). (e) [4 points] For the given parameters in (c), determine if the circuit is overdamped, underdamped, or critically damped. (f) [8 points] Use your results from (e) to find the response of i (L) for t>0. (g) [5 points] If we replace the 8 Ω resistor with a 4Ω resistor (R = 4Ω), determine if the circuit is overdamped, underdamped, or critically damped. Problem 2 [33 points] The circuit of Fig.2 operates in the sinusoidal steady-state. (a) [2 points] Transfer the circuit into the phasor domain and, in the provided diagram clearly label values of all components. (b) [3 points] Draw the phasor domain equivalent circuit for the case when only the current source is active, i.e. the voltage source is turned off. i) [6 points] Find the phasor Vx , c1rresponding to the sole contribution of the current source to Vx . ii) [5 points] Find the phasor Ix , c1rresponding to the sole contribution of the current source to the phasor current Ix. (c) [3 points] Draw the phasor domain equivalent circuit for the case when only the voltage source is active i) [6 points] Find the phasor Vx , co2responding to the sole contribution of the voltage source to Vx . ii) [5 points] Find the phasor Ix , corr2sponding to the sole contribution of the voltage source to the phasor current Ix. (d) [3 points] Find v (t), xnd i (t) x Problem 3 [34 Points] In the following, all OP-AMPs are ideal and no energy is stored initially in any of these circuits. 0.01 μF 200 kΩ 10 kΩ
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