ECE 301
HW #7
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Due: November 8, ‘07
Name_______________________
Use engineering paper. Work only on one side of the paper. Use this sheet as your cover sheet, placed on
top of your work and stapled in the top left-hand corner. Number the problems at the top of the page, in
the center of the sheet. Do neat work. Underline your answers. Show how you got your equations.
Be sure to show how you got your answers. Each problem counts 10 points.
This is a drill exercise to prepare you for AC circuits. You will need a TI 86 calculator or equivalent
to do this type of math, proficiently. If you do not own one you need to borrow or buy one, immediately.
(1) Calculator not necessary for this problem. Use the graphical method introduced in class and
presented in the text (page 374) to express the following as cosine functions.
(i)
(ii)
(iii)
80sin(wt – 30o)
– 100sin(wt + 120o)
200sin(wt + 60)
(2) Work the following problem by the methods indicated.
(a) Use (a + jb) algebra and trig to determine the value of the following
function in polar form.
(2  j 4)  (6  j8)
(3  j10)
(b) Determine the value of the function above, expressed in polar form, by direct use of your
calculator.
(3) Using your calculator directly, convert each of the following functions to polar form and plot (sketch)
them on a graph. Which function is leading?
(a)
V1 
(24  j17)(19  j8)
(2  j 6)(8  j14)
(b)
V2 
5060o (45  j 25)
(6  j14)
(4) Use your calculator, directly, to find the following. Express in polar form.
A
(2  j3)(12  j18)
(3  j8)(6  j 4)
Ans: A = 1.266-35.75o
(5) Use your calculator, directly, to find the following. Express in rectangular form.
A
630o (2  j 4)
(6  j12)(2  45o )
(6) Use your calculator, directly, to find the following. Express in polar form.
A
(3  j 6)  (9  j8)
14  30o  2060o
(7) Convert the following to phasors. Use a cosine reference.
(a)
(b)
(c)
(d)
-50sin(100t-30o)
200cos(300t+60o)
–200cos(300t+60o)
400sin(wt+30)