Answered: x(t) = 3 + 4 cos(20nt +30) + 2…

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Electrical Engineering

x(t) = 3 + 4 cos(20nt +30) + 2 sin(60nt) - 4 cos(70nt)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Capacitor

The capacitor is an element used to store electrical energy in the electrical field. A capacitor is a form of passive energy.

Question

i need the answer quickly

Phasor Signals and Spectra
A useful periodic signal in system analysis is the signal
x(t) = Aej(@ot+0),
Im
wol+0
A cos (@of +0)
Re
-∞<t<∞
MT.
Im
Phase
@of+0
@ol+0
The rotating phasor Ae(+) can be related to a real, sinusoidal signal A cos(@ot+0)
in two ways. The first is by taking its real part,
fo
A cos (wol +0)
x(t) = A cos(@ot + 0) = Rex(1)
= Re Ae/(1+0)
112
-Re
and the second is by taking one-half of the sum of x(1) and its complex conjugate,
A cos(@pt + 0) = x(1) + X* (1)
1
Aej (@₂²+0) + = Ae¯j(1+0)
2
Example:
Sketch the single-sided and double-sided spectra of
Amplitude
Amplitude
A
I hj
A
fo
0
fo
x(t) = 3 + 4 cos(20nt +30) + 2 sin(60nt) - 4 cos(70nt)
cose
fo
A Acose+jAsino
Phase
0
fo

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