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Homework Statement
http://imageshack.us/a/img834/8450/4y0t.jpg
Given V(s)t = 100cos100t volts, find the average power supplied by the source and the current i2t in the network.
Homework Equations
V = IR
V = IZ
Z = V/I
inductor impedance: ZL = ωLj
capacitor impedance: Zc = -1j/ωc
j*j = -1
Average power = (1/2)VmIm
The Attempt at a Solution
ω = 100
L = 50 x 10-3
ZL = ωLj
ZL = (50 x 10-3)(100)
ZL = 5jΩ
C = (1 x 10-3)F
capacitor impedance: Zc = -1j/ωc
so
Zc = -1j/(1 x 10-3)(100)
Zc = -10jΩ
Now: 15Ω || 1mF
=[ (1/15) + (-1/10j) ]-1; LCD:
= (2j/30j - 3/30j)-1
= (2j - 3/30j)-1
= 30j/(2j - 3); multiply by conjugate:
=> 30j/(2j - 3) * (-2j-3)/(-2j-3)
= -60j2 - 90j/(-4j2 - 6j + 6j + 9; now multiply out j^2s
= 60 - 90j / 13
= (4.615 - 6.92j)Ω; add to rest of impedance
Z(total) = (14.615 - 1.92j)Ω
I am really bad with the formula so not sure how to go about getting P(avg) now.
TO get I of the whole circuit I think just do I = V/Z, and then do (1/2)VmIm ?
but forgot how to get the sinusoidal function (ie 100cos100t) in phasor form
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