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Unit 11 Practice Sheet: Sinusoids and Phasors
1. The following questions refer to the waveform shown below.
a. How many cycles of the waveform are shown in this diagram?
b. What is the waveform’s period?
c. What is the waveform’s frequency?
d. What is the waveform’s angular frequency?
e. What is the waveform’s amplitude?
f. What is the waveform’s peak-to-peak value?
g. What is the waveform’s instantaneous value at t = 2 ms? At t = 3.5 ms?
2. The following questions refer to the waveforms shown below.
a. Which waveform (the taller or the shorter) leads the other one?
b. Which waveform (the taller or the shorter) lags the other one?
c. By what angle does the one waveform lead the other one?
EGR 2201
Reeder
EGR 2201 Unit 11 Practice sheet - 2
3. The following questions refer to the sinusoid expressed by v(t) = 50 cos(200t + 30°) V.
a. What is the waveform’s amplitude?
b. What is the waveform’s peak-to-peak value?
c. What is the waveform’s angular frequency?
d. What is the waveform’s frequency?
e. What is the waveform’s period?
f. What is the waveform’s phase angle in degrees?
g. What is the waveform’s phase angle in radians?
h. What is the waveform’s instantaneous value at t = 3 ms? At t = 6 ms?
4. The following questions refer to the following two sinusoids:
v1(t) = 50 cos(200t + 12°) V, v2(t) = 8 cos(200t + 30°) V.
a. What is v1’s phase angle (in degrees)?
b. What is v2’s phase angle (in degrees)?
c. Which voltage leads the other one, and by how many degrees?
d. Which voltage lags the other one, and by how many degrees?
5. Express the following sinusoids using the cosine function instead of the sine function:
a. v1(t) = 10 sin(200t + 40°) V
b. v2(t) = 20 sin(500t − 15°) V
c. v3(t) = −15 sin(100t + 10°) V
d. v4(t) = −40 sin(80t − 50°) V
EGR 2201 Unit 11 Practice sheet - 3
6. Locate the following numbers in the complex plane:
a. z1 = 3 + j4
b. z2 = −2 + j5
c. z3 = −8 − j4
d. z4 = 4 − j6
7. Express the previous question’s numbers in polar form.
8. Express the following numbers in rectangular form:
a. z5 = 3 ∠−30°
b. z6 = 5 ∠40°
9. Complete the table. You’ve already found some of these answers in previous questions.
Number
Rectangular form
Polar form
Exponential form
z1
3 + j4
z5
3 ∠−30°
z6
5 ∠40°
10. Using your table, perform the following operations and express each result in polar form:
a. z1 + z5 =
b. z5 / z6 =
c. (z1 − z6) / z5 =
d. (z1 + z6) z5 =
EGR 2201 Unit 11 Practice sheet - 4
11. Write the MATLAB command for defining each of the following numbers:
a. z1 = 3 + j4
b. z5 = 3 ∠−30°
c. z6 = 5 ∠40°
12. Write the MATLAB command to perform each of the following operations. I want the
answer in polar form, so include commands that will give you the magnitude and angle (in
degrees) of each result:
a. z1 + z5
b. z5 / z6
c. (z1 − z6) / z5
d. (z1 + z6) z5
13. Perform the following operation and express the result in polar form:
6∠30° + 5 − 3
2+ 4
14. Write the MATLAB command for finding the answer to the previous question. Also write
commands that will give the magnitude and angle (in degrees) of the result.
EGR 2201 Unit 11 Practice sheet - 5
15. Practice Problem 9.4 from the textbook: Express these sinusoids as phasors. (Or, stated
using fancier terminology, transform these sinusoids from the time domain to the phasor
domain.)
(a) v = 7 cos(2t + 40°) V
(b) i = −4 sin(10t + 10°) A
16. Practice Problem 9.5 from the textbook: Find the sinusoids corresponding to these phasors.
(Or, stated using fancier terminology, transform these sinusoids from the phasor domain to
the time domain.)
(a) V = −25∠40° V
(b) I = j(12 − j5) A
17. Practice Problem 9.6 from the textbook: If v1 = −10 sin(ωt − 30°) V and
v2 = 20 cos(ωt + 45°) V, find v = v1 + v2.
18. Problem 9.30 from the textbook: If a voltage v = 100 cos(60t + 20°) V is applied to a 40-kΩ
resistor, find the current through the resistor.
19. Example 9.8 from the textbook: If the voltage v = 12 cos(60t + 45°) V is applied to a 0.1-H
inductor, find the current through the inductor.
EGR 2201 Unit 11 Practice sheet - 6
20. Practice Problem 9.8 from the textbook: If the voltage v = 10 cos(100t + 30°) V is applied to
a 50-μF capacitor, find the current through the capacitor.
21. Find the impedances of the resistor, the inductor, and the capacitor in the three previous
questions. Express each impedance in both polar form and rectangular form.
(a) ZR =
(b) ZL =
(c) ZC =
22. Find the admittances of the resistor, the inductor, and the capacitor in the previous question.
Express each admittance in both polar form and rectangular form.
(a) YR =
(b) YL =
(c) YC =
23. Example 9.9 from the textbook: Find i(t) and v(t) in the circuit shown below.
EGR 2201 Unit 11 Practice sheet - 7
24. Problem 9.59 from the textbook: Find Zin in polar form for this circuit. Assume ω = 10 rad/s.
(Hint: First redraw the circuit in the phasor domain.)
25. Problem 9.60 from the textbook: Find Zin in polar form for the circuit shown below. (Note
that this drawing, unlike the previous one, shows the circuit in the phasor domain.)
26. Problem 9.39 from the textbook: Find Zeq and I in polar form for the circuit shown below.
EGR 2201 Unit 11 Practice sheet - 8
27. Problem 9.41 from the textbook: Find is(t) in the circuit shown below.
28. Find vo(t) in the same circuit (Hint: In the phasor domain, use the current-divider rule to find
the current IC through the capacitor.)