solve the Hw. Example: Determine the power and the rms value of the following(a)x(t) = C cos (wot + 0)(b)x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂)Solution:(a)x(t) = C cos (wot + 0)It is a periodic signal with period To = 27/wo. The suitable measure of this signal is its power.1 T/21 T/2P ==P =x² (t)dt-T/2C² -T/22TP=2²23=[1 + cos(2wot+20)] dtC² cos² (wot+0)dt=T/2-T/21 dt +-T/2W₁ W2cos(2wot +20) dt-T/2This show that a sinusoid of amplitude C has a power C²/2 regardless of the valueof its frequency w(wo‡0) and phase 0.CPrms==HW: If the signal frequency is 0 (dc or a constant signal of amplitude C), show that the power is C².

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Answered: Example: Determine the power and the…

Example: Determine the power and the rms value of the following (a) x(t) = C cos (wot + 0) (b) x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂) W₁ W₂

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter2: Fundamentals

Section: Chapter Questions

Problem 2.2MCQ: If the rms phasor of a voltage is given by V=12060 volts, then the corresponding v(t) is given by...

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Question

solve the Hw.

Example: Determine the power and the rms value of the following
(a)
x(t) = C cos (wot + 0)
(b)
x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂)
Solution:
(a)
x(t) = C cos (wot + 0)
It is a periodic signal with period To = 27/wo. The suitable measure of this signal is its power.
1 T/2
1 T/2
P ==
P =
x² (t)dt
-T/2
C² -T/2
2T
P=2²23
=
[1 + cos(2wot+20)] dt
C² cos² (wot+0)dt
=
T/2
-T/2
1 dt +
-T/2
W₁ W2
cos(2wot +20) dt
-T/2
This show that a sinusoid of amplitude C has a power C²/2 regardless of the value
of its frequency w(wo‡0) and phase 0.
C
Prms
==
HW: If the signal frequency is 0 (dc or a constant signal of amplitude C), show that the power is C².

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