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real, reactive, and complex power in AC circuit "PLEASE HELP ME"

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Date Posted: 7/20/2008 4:39:17 PM  Status: Live
real, reactive, and complex power in AC circuit "PLEASE HELP ME"
Course Textbook Chapter Problem
N/A Circuits by Franco 12 21
Question Details:
a) Find the real, reactive, and complex power delivered by the source.
b) What reactive element must be connected in parallel with the source to make its power factor 1?
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Oracle
Karma Points: 9,336
Date Posted: 7/20/2008 11:43:45 PM  Status: Live
Asker's Rating: Lifesaver   
Response:
Given
V = 50 cos(10t)
V= 35.36 /_0o V
ω = 10 rad/sec
XC = 1/ωC =1/(10)(1/300) = 300 / 10 = 30Ω
XL = ωL = (10)(3) = 30Ω
Impedance of the circuit is
Z = 10 + [ -jXC || (30 +jXL)]
The current from the source will be
a)
Vrms = 35.36V
Irms = 0.707A
φ = -37o
Real power P = Vrms Irms cosφ = (35.36)(0.707)[cos(-37)] = 20W
Reactive power Q = Vrms Irms sinφ = (35.36)(0.707)[sin(-37)] = -15 VAR
Complex power delivered is
S = P + jQ
S = 20-j15
or
S = 25/_-37o VA
 
Let the reactive element connected across the source have a reactance X
Then the impedance of the circuit will be
Z' = jX + Z
Z' = jX + 40-j30
|Z'| = √(40)2 + (X-30)2
Phase difference is
To make the power factor 1, that is
pf = cosφ =1
φ should be 0o
then
X = 30Ω
The reactance is jX = 30Ω, hence an inductance should be connected in parallel
 
 
 
 
 
 
aash's Comment:
Thanks man



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