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Unformatted text preview: UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAMINATION, April 2007
First Year — Engineering Science
ECE159HIS — Electric Circuit Fundamentals
Exam Type: A Examiners  D. Lavers and B. Wang STUDENT NO: Instructions: Answer all 5 questions Nonprogrammable calculators allowed Use the back of the previous page for rough work Do not unstaple this exam booklet Name: Student Number:
Question 1 [10 points] 12v
V1 V0 a) Develop the equations (ﬁnal form) for the two nodal potentials identiﬁed in the ﬁgure (2 marks). b) Detemtine the output potential V0. Express your answer as an integer or fraction, as appropriate
(4 marks). 0) Detennine how much power is supplied or absorbed by each source, and state whether it is
SUPPLIED or ABSORBED (4 marks). Page 2 of 8 Name: Student Number:
Question 2 [10 marks] 12V 2k!) a) Find the Thevenin equivalent voltage (Vm) to the left of the nodes AB (3 marks). b) Calculate the Thevenin equivalent resistance (Rm), to the left of the nodes AB (4 marks). c) Calculate the voltage on the load resistor (V0) (1 mark). (1) Draw the Norton equivalent circuit and specify the values of IN and RN to the left of nodes AB
(2 marks). Page 3 of 8 Name: Student Number:
Question 3 [10 marks] At time t = 0, the switch shown in the ﬁgure is opened. Solve for iL(0“), vc(0"), TL, 10 , iL(t), and vc(t)
for t > 0. 29 IQ t H
O Page 4 of 8 Name: Student Number:
Question 4 [10 marks] The source voltage vs(t) has an rms amplitude of 12 V, a frequency of 3 l 83 Hz and a phase angle of 0°.
a) Determine the output voltage vo(t), amplitude and phase (6 marks). b) Determine the complex power supplied/absorbed by the dependent source (4 marks). Page 5 of 8 Name: Student Number:
Question 53 [3 marks] Vs“) (V) 12345t(ms) Determine the time average power supplied by the voltage source vs(t). Page 6 of 8 R H 4Q Name: Student Number:
Question 5b [3 marks] Determine the sdomain voltage transfer function Vl(s)Ns(s) for the circuit shown in the ﬁgure. R L
Ill vs(t) 3 R2 Page 7 of 8 Name: Student Number:
Question 5c [4 points} Consider the series RLC circuit shown in the ﬁgure. The sinusoidal source voltage has an amplitude of 2 V peak, but frequency a) can be varied:
vs(t) = 2 cos(cot) “0 C L The capacitor has a known value of 20 uF. As the frequency (0 is varied, it is found that the greatest current V (t) R amplitude is obtained at a) = 1000 rad/s. At this frequency, the
current amplitude is found to be 20 A peak. Determine the R, L, and NJ. Page 8 of 8 ...
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 Winter '08
 B.wang
 student number, Electrical network, Thévenin's theorem, Voltage source, Norton's theorem, Engineering Science

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