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Circuits and Systems II - Homework 2 Practice Problems | ECE 202, Assignments of Microelectronic Circuits

Michigan State University (MSU)Microelectronic Circuits

Material Type: Assignment; Class: Circuits and Systems II; Subject: Electrical & Computer Egr; University: Michigan State University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 07/23/2009

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koofers-user-z97 🇺🇸

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ECE202(Fall2007)
HomeworkNo.2
Due:Friday,09/07/2007
(P.1)[20pts.]Asinusoidalvoltagesignal,v(t),hastheform:
󰇛󰇜
cos󰇛2󰇜V
ThesignalhasaperiodofT=5µs.Att=0theamplitudeis‐31.42V.Thesignalwaveform
reachesitsfirstpositivepeakaftert=0att=3µs.
a) Sketchthesignal,v(t),byhandandindicateallpertinentinformation
accordingly.(8pts)
b) Whatisthesignalfrequency,f,inhertz?(2pt)
c) If
φ
ispositive,towardswhichdirectionhasthesignalbeenshifted?(1pt)
d) Basedonyouranswertoc),whatisthephaseangle,
φ
,indegrees?(7pts)
e) Whatistheamplitude,VA,ofthesignal?(2pt)
(P.2)[15pts.]Forthefollowingtwosinusoidalsignals:
󰇛󰇜10cos
󰇛50°󰇜V
󰇛󰇜12sin
󰇛10°󰇜V
a) Convertthesignalsintophasors(6pts)
b) Findtheanglebetweenthesignalsusingphasors.(2pts)
c) Sketchtheanglebetweenthesignalsgraphicallyusingphasors(6pts)
d) Indicatewhichsignalisleading(i.e.,hasalargeranglemeasuredcounter‐clockwise
fromthepositive“Re”axis).(1pt)
(P.3)[15pts.]Usingthephasorapproach,determinethesteady‐statecurrent,i(t),ina
circuitdescribedbytheequation
4󰇛󰇜 8󰇛󰇜 3󰇛󰇜
 50cos 󰇛4 75°󰇜

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Download Circuits and Systems II - Homework 2 Practice Problems | ECE 202 and more Assignments Microelectronic Circuits in PDF only on Docsity!

ECE 202 (Fall 2007) Homework No. 2 Due: Friday, 09/07/

(P.1) [20 pts.] A sinusoidal voltage signal, v(t) , has the form:

ܸൌ ሻݐሺݒ (^) ௠ cosሺ2 ݐ݂ߨ൅ ߶ ሻ^ V

The signal has a period of T = 5 μ s. At t = 0 the amplitude is ‐31.42 V. The signal waveform reaches its first positive peak after t = 0 at t = 3 μ s.

a) Sketch the signal, v(t) , by hand and indicate all pertinent information accordingly. (8 pts) b) What is the signal frequency, f , in hertz? (2 pt)

c) If φ is positive, towards which direction has the signal been shifted? (1 pt)

d) Based on your answer to c), what is the phase angle, φ, in degrees? (7 pts)

e) What is the amplitude, VA, of the signal? (2 pt)

(P.2) [15 pts.] For the following two sinusoidal signals:

ݒଵ ሺݐሻ ൌ െ10 cosሺ ݐ߱൅ 50 °^ ሻ^ V

ݒଶ ሺݐሻ ൌ 12 sinሺ ݐ߱െ 10 °^ ሻ V

a) Convert the signals into phasors (6 pts) b) Find the angle between the signals using phasors. (2 pts) c) Sketch the angle between the signals graphically using phasors (6 pts) d) Indicate which signal is leading (i.e., has a larger angle measured counter‐clockwise from the positive “ Re” axis). (1 pt)

(P.3) [15 pts.] Using the phasor approach, determine the steady‐state current, i(t) , in a circuit described by the equation

݅݀3 െ ݐ݀ሻݐሺ ݅න 8 ൅ ሻݐሺ݅

ݐ ൌ 50cos ሺ4 ݐ൅ 75°ሻ