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Homework Statement
http://imageshack.us/a/img4/5259/wn5b.jpg
Find the average power absorbed by the resistor in the circuit
if v1(t) = 10cos(377t + 60°)V
and v2(t) = 20cos(377t + 120°)V
Homework Equations
average power = (1/2)Vmax*Imax*cosø
x=rcosθ
y=rsinθ
mag = (r2 + j2)1/2
θ = arctan(j/r)
The Attempt at a Solution
v1(t) = 10cos(377t + 60°)V; = (10∠60°)V; = (5 + 8.66j)V
v2(t) = 20cos(377t + 120°)V; = (20∠120°)V; = (-10 + 17.32j)V
Z = 1Ω; = (1 ∠ 0°)Ω
Vtotal = v1 - v2 = 5 + 8.66j - (-10 + 17.32j)
Vtotal = (15 - 8.66j) V
Vtotal = (17.32 ∠-30°)V
and I think these are all max values so:
I = V/Z
I = (17.32∠-30°)/(1∠0°)
I = (17.32∠-30°)A
Avg power = (1/2)(17.32)(17.32)(cos 0) = 150W
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