Technological University of the Philippines
COLLEGE OF ENGINEERING
Electronics Engineering Department
ACECE 6
Circuits 2
2nd Semester, AY 2022-2023
Assignment No. 1
Sinusoids and Phasors
SURNAME, GIVEN NAME, M.I .
BSECE 1
Date Submitted:
GRADE
ENGR. GILFRED ALLEN M. MADRIGAL
Instructor
1. Given the sinusoidal voltage
𝑣(𝑡) = 50 cos(30𝑡 + 10°) 𝑉, find:
a. The amplitude Vm
b. The period T
c. The frequency f and
d. 𝑣(𝑡) at 𝑡 = 10 𝑚𝑠
connected in parallel with a 1.25 H
inductor.
9. What value of 𝜔 will cause the
forced response, 𝑣0, in Figure 1 to be
zero?
2. Evaluate these determinants:
10 + 𝑗6
2 − 𝑗3
|
−1 + 𝑗
20∠ − 30° −4∠ − 10°
b. |
|
16∠0°
3∠ − 45°
1 − 𝑗 −𝑗
0
1
−𝑗 |
c. | 𝑗
1
𝑗 1+𝑗
a. |
−5
3. Combine the following sinusoidal
functions into a single trigonometric
expression:
a. 𝑦 = 30 cos(200𝑡 − 160°) + 15 cos(200𝑡 + 70°)
b. 𝑦 = 90 sin(50𝑡 − 20°) + 60 cos(200𝑡 − 70°)
c. 𝑦 = 50 cos(5000𝑡 − 60°) + 25 sin(5000𝑡 +
Figure 1
10. Find the current 𝑖𝑜 in the circuit
shown in Figure 2 when:
a. 𝜔 = 1 𝑟𝑎𝑑/𝑠
b. 𝜔 = 5 𝑟𝑎𝑑/𝑠
c. 𝜔 = 10 𝑟𝑎𝑑/𝑠
110°) − 75 cos(5000𝑡 − 30°)
d. 𝑦 = 10 cos(𝜔𝑡 + 30°) + 10 sin 𝜔𝑡 + 10 cos(𝜔𝑡 +
150°)
4. Evaluate the following:
a. 3 cos(20𝑡 + 10°) − 5cos(20𝑡 − 30°)
b. 40 sin 50𝑡 + 30cos(50𝑡 − 45°)
c. 20 sin 400𝑡 + 10cos(400𝑡 + 60°) −
5 sin(400𝑡 − 20°)
Figure 2
11. If 𝑖𝑠 = 5 cos(10𝑡 + 40°)𝐴 in the circuit
of Figure 3, find 𝑖𝑜.
5. Two voltages 𝑣1 and 𝑣2 appear in
series so that their sum is 𝑣 = 𝑣1 + 𝑣2.
If
𝑣1 = 10 cos(50𝑡 − 𝜋⁄3)𝑉
and
𝑣2 =
12 cos(50𝑡 + 30°)𝑉, find 𝑣.
6. An alternating voltage is given by
𝑣(𝑡) = 55 cos(5𝑡 + 45°)𝑉. Use phasors to
𝑡
𝑑𝑣
find 10𝑣(𝑡) + 4 − 2 ∫ 𝑣(𝑡)𝑑𝑡. Assume that
12. Find 𝑣 (𝑡) in the circuit of Figure
the value of the integral is zero at
𝑡 = −∞.
4 if the current 𝑖𝑥 through the 1-Ω
resistor is 0.5 sin 200𝑡 𝐴.
𝑑𝑡
−∞
Figure 3
𝑠
7.
Find
𝑣(𝑡)
in
the
following
integrodifferential equations
using
the phasor approach:
a. 𝑣(𝑡) + ∫ 𝑣 𝑑𝑡 = 10 cos 𝑡
b. 𝑑𝑣 + 5𝑣(𝑡) + 4 ∫ 𝑣 𝑑𝑡 = 20 sin(4𝑡 + 10°)
𝑑𝑡
8. Find the values of resistance and
inductance that when connected in
series will have the same impedance at
4 krad/s as that of a 5 kΩ resistor
Figure 4
13. Find 𝑣𝐴(𝑡) in Figure 5.
Figure 5
14. The phasor current Ib in the circuit
shown in Figure 6 is 25∠0° 𝑚𝐴.
a. Find Ia, Ic, and Ig.
b. If
𝜔 = 1500 𝑟𝑎𝑑/𝑠,
write
expressions for 𝑖𝑎(𝑡), 𝑖𝑏(𝑡), and
𝑖𝑔(𝑡).
Figure 6
15. Calculate the value of 𝑍𝑎𝑏 in the
network of Figure 7.
Figure 7