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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