Linear Circuit Quiz
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eeng_3305_final_exam.pdf
EENG 3305 Linear Circuit Analysis II
Final Exam
December 14, 2013
Name:
Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Please complete the exam in pencil and clearly denote the final answer. Except where trivial, show all work!
Question Points Bonus Points Score
1 10 0
2 5 0
3 5 0
4 5 0
5 5 0
6 10 0
7 10 0
8 4 0
9 6 0
10 10 0
11 5 0
12 10 0
13 5 0
14 10 0
15 0 8
16 0 7
Total: 100 15
EENG 3305 Final Exam - Page 1 of 11 December 12, 2013
1. [10 points] Determine the Fourier coefficients a1, a2, a3, a4 and b1, b2, b3, b4 of the rectified cosine wave shown below
−2 2 4 6 8 10 12
2
4
t
f(t)
EENG 3305 Final Exam - Page 2 of 11 December 12, 2013
2. [5 points] If the rectangular pulse shown below is applied to the circuit, also shown below, find v0 at t = 1s.
1 2 3
2
4
6
t
vs(t)
+ −vs(t)
2 Ω
2 Ω 1 H
+
−
v0
Page 2
EENG 3305 Final Exam - Page 3 of 11 December 12, 2013
3. [5 points] Find the transfer function Io(ω)
Is(ω) for the following circuit
is(t) 2 Ω 1 H 4 Ω
i0(t)
Page 3
EENG 3305 Final Exam - Page 4 of 11 December 12, 2013
4. [5 points] Obtain the Fourier Transform of the following function
−4 −1 1 4
−2
2
t
vs(t)
Page 4
EENG 3305 Final Exam - Page 5 of 11 December 12, 2013
5. [5 points] Use the convolution integral to find e−2tu(t) ∗ e−3tu(t)
6. [10 points] Given that the circuit is initially at rest use the Laplace transform to solve the differential equation
d2v(t)
dt2 + 12
dv(t)
dt + 35v(t) = e−2t
.
Page 5
EENG 3305 Final Exam - Page 6 of 11 December 12, 2013
7. For the circuit below
+ −60u(t)
2 Ω
+ − vo(t)
2 H 2 Ω
(a) [2 points] Write the integrodifferential equation for vo(t) assuming no initial condi- tions in the circuit.
(b) [2 points] Convert the equation you obtained in the previous part to the Laplace domain.
(c) [2 points] Find the transfer function if the output of interest is the 1Ω resistor voltage.
(d) [2 points] Calculate the impulse response of the system.
(e) [2 points] Calculate the step response of the system.
Page 6
EENG 3305 Final Exam - Page 7 of 11 December 12, 2013
8. A circuit consisting of a coil with inductance 10mH and resistance 20Ω is connected in series with a capacitor and a generator with an RMS voltage of 120V. Find:
(a) [2 points] the value of the capacitance that will clause the circuit to be in resonance at 15kHz
(b) [2 points] the current through the coil at resonance
9. The circuit parameters for a series RLC bandstop filter are R = 2kΩ, L = 1H, C = 40pF. Calculate
(a) [2 points] the center frequency
(b) [2 points] the half-power frequencies
(c) [2 points] the quality factor
Page 7
EENG 3305 Final Exam - Page 8 of 11 December 12, 2013
10. [10 points] Find the y parameters for the following circuit
4 Ω 6 Ω
ix
2 Ω
3ix
11. [5 points] A balanced delta-connected load has line current Ia = 5 −30◦A. Find the phase currents IAB, IBC, ICA.
Page 8
EENG 3305 Final Exam - Page 9 of 11 December 12, 2013
12. Three 230V generators form a delta-connected sourced that is connected to a balanced delta-connected load of ZL = 10 + j10 Ω per phase.
(a) [5 points] Determine the value of IAC
(b) [5 points] Is the load inductive or capacitive?
13. [5 points] A three-phase balanced system with a line voltage of 300V RMS feeds a delta- connected load with ZP = 75 70
◦Ω. Find the line current.
Page 9
EENG 3305 Final Exam - Page 10 of 11 December 12, 2013
14. [10 points] Sketch the magnitude and phase plots for
G(s) = s
(s + 2) 2
(s + 10)
Page 10
EENG 3305 Final Exam - Page 11 of 11 December 12, 2013
15. [8 points (bonus)] In the ideal transformer circuit in the circuit below, find Vo and the complex power supplied by the source
+ −240 0◦
2 Ω 16 Ω
−j24
1 : 8
16. [7 points (bonus)] Find the input impedance of the circuit below and the current from the voltage source
+ −240 60◦
4 Ω 16 Ω
6 Ω
j4Ω
j3Ω
Page 11
