ework: Obtain the sinusoids corresponding to each of the following phasors: 4.12 (a) Vi = 60/15°, w = ! (b) V2 = 6+ j8, w = 40 %3D (c) I = 2.8e-ja/3_ (d) I2 = -0.5 - j1.2, o = 10 °, w = 377 %3D %3D %3D ver: |(a)= 60 cos(t + 15°), (b)= 10 cos(40t + 53.13°), (c)= 2.8 cos(377t – T/3), (d)= 1.3 cos(10³t + 247.4°)

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Author:Robert L. Boylestad
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Question
(a) 8 cos(5t - 30°) + 6 cos 5t
(b) 20 cos(120t + 45°) – 30 sin(1207t + 20)
(c) 4 sin 8t + 3 sin(8t - 10°)
nswer:
(a)= 13.533 cos(5t + 342.81°), (b)= 42.51 cos(120rt + 84.76°), (c)= 6.974 cos(8t + 265.72°)
-Qar University/Department of Electrical and Electronic Engineering-Lectures are prepared by M.Sc. Ali Kareem Page 13
2015-2016
ge: Fundamentals of Electrical Engineering Chapter 14 – Sinusoids and Phasors
nework: Obtain the sinusoids corresponding to each of the following phasors:
4.12
(a) Vi = 60/15°, w = 1
(b) V2 = 6+ j8, w = 40
(c) I = 2.8e"j7/3, w = 377
(d) I2 =-0.5- j1.2, w = 10
(a)= 60 cos(t+ 15°), (b)= 10 cos(40t + 53.13°), (c)= 2.8 cos(377t – Tt/3),
|(d)= 1.3 cos(10³t + 247.4°)
ver:
nework: Find v(t) in the following integrodifferential equations using the phasor approach:
_4.13
(a) v(t) +
v dt = 10 cos t
dv
(b)
+ 5v(t) +4
v dt = 20 sin(4t + 10°)
dt
wer:
(a)= 7.071 cos(t + 45°), (b)
3.43 cos(4t - 110.96°)
mework: Using phasors, determine i(t) in the following equations::
14.14
di
(а) 2
+ 3i (1) = 4 cos(2t – 45°)
dt
Sidt+
di
+ 6i (t) = 5 cos(5t + 22°)
(b) 10
(a)= 0.8 cos(2t –- 98.13°), (b)
0.745 cos(5t - 4.56°)
wer:
mework: The loop equation for a series RLC circuit gives:
di
+ 2i +
dt
Assuming that the value of the integral att =-00 is zero, find i(t) using the phasor method.
14.15
i dt :
= cos 2t
swer:
0.4 cos(2t- 36.87°)
-mework: A parallel RLC circuit has the node equation:
dv
+ 50v + 100
dt
14.16
v dt = 110 cos(377t – 10°)
Determine v(t) using the phasor method. You may assume that the value of the integral at t =-00 is
zero.
V
110Z-10°, 0= 377
jo
lution:
joV + 50V +100-
jl00
V j377+50-
377
=110Z-10°
V (380.6282.45°) = 1102-10°
V = 0.289Z-92.45°
Therefore, v(t)
0.289 cos(377t- 92.45°).
-Qar University/Department of Electrical and Electronic Engineering-Lectures are prepared by M.Sc. Ali Kareem Page 14
Transcribed Image Text:(a) 8 cos(5t - 30°) + 6 cos 5t (b) 20 cos(120t + 45°) – 30 sin(1207t + 20) (c) 4 sin 8t + 3 sin(8t - 10°) nswer: (a)= 13.533 cos(5t + 342.81°), (b)= 42.51 cos(120rt + 84.76°), (c)= 6.974 cos(8t + 265.72°) -Qar University/Department of Electrical and Electronic Engineering-Lectures are prepared by M.Sc. Ali Kareem Page 13 2015-2016 ge: Fundamentals of Electrical Engineering Chapter 14 – Sinusoids and Phasors nework: Obtain the sinusoids corresponding to each of the following phasors: 4.12 (a) Vi = 60/15°, w = 1 (b) V2 = 6+ j8, w = 40 (c) I = 2.8e"j7/3, w = 377 (d) I2 =-0.5- j1.2, w = 10 (a)= 60 cos(t+ 15°), (b)= 10 cos(40t + 53.13°), (c)= 2.8 cos(377t – Tt/3), |(d)= 1.3 cos(10³t + 247.4°) ver: nework: Find v(t) in the following integrodifferential equations using the phasor approach: _4.13 (a) v(t) + v dt = 10 cos t dv (b) + 5v(t) +4 v dt = 20 sin(4t + 10°) dt wer: (a)= 7.071 cos(t + 45°), (b) 3.43 cos(4t - 110.96°) mework: Using phasors, determine i(t) in the following equations:: 14.14 di (а) 2 + 3i (1) = 4 cos(2t – 45°) dt Sidt+ di + 6i (t) = 5 cos(5t + 22°) (b) 10 (a)= 0.8 cos(2t –- 98.13°), (b) 0.745 cos(5t - 4.56°) wer: mework: The loop equation for a series RLC circuit gives: di + 2i + dt Assuming that the value of the integral att =-00 is zero, find i(t) using the phasor method. 14.15 i dt : = cos 2t swer: 0.4 cos(2t- 36.87°) -mework: A parallel RLC circuit has the node equation: dv + 50v + 100 dt 14.16 v dt = 110 cos(377t – 10°) Determine v(t) using the phasor method. You may assume that the value of the integral at t =-00 is zero. V 110Z-10°, 0= 377 jo lution: joV + 50V +100- jl00 V j377+50- 377 =110Z-10° V (380.6282.45°) = 1102-10° V = 0.289Z-92.45° Therefore, v(t) 0.289 cos(377t- 92.45°). -Qar University/Department of Electrical and Electronic Engineering-Lectures are prepared by M.Sc. Ali Kareem Page 14
Evaluate these complex numbers:
(a) [(5+ j2)(-1+ j4) – 5/60°]*
10 + j5 + 3/40
(b)
+ 10/30°
-3+ j4
(a) -15.5 j13.67, (b) 8.293 + j2.2.
Transcribed Image Text:Evaluate these complex numbers: (a) [(5+ j2)(-1+ j4) – 5/60°]* 10 + j5 + 3/40 (b) + 10/30° -3+ j4 (a) -15.5 j13.67, (b) 8.293 + j2.2.
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