- #1
RobJob
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Homework Statement
SOURCE:
v(t) = (311)cos(314t) [v]
IN SERIES WITH:
R = (0.3) [Ω]
L = j(0.7) [Ω]
"load" = 2.5 + j(1.0) [Ω]
Homework Equations
Find the instantaneous current, and the phasor current.
The Attempt at a Solution
(1.) I first found the frequency of the source:
(314) / (2*pi) ≈ 50 Hz.
(2.) Figure out the value of the inductor:
jωL = j(0.7) => j(50)L = j(0.7) => L = (0.7/50) = 14 [mH]
(3.) I started doing KVL around the loop:
(-311)cos(314t) + (0.3)(i(t)) + (14e-3) (di/dt) ...
Then I didn't know what to do for the "load." It isn't specified if it's a capacitor/inductor/mix, and I'm not sure how to go from 2.5 + j(1.0) [Ω] to something I can use in the time domain? Is it just the real part of that value?
So... (-311)cos(314t) + (0.3)(i(t)) + (14e-3) (di/dt) + 2.5 = 0 ?
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(1.) For the phasor I found the total impedance:
0.3 + j(0.7) + 2.5 + j(1.0) = 2.8 + j1.7 = 3.27∠31.26 [Ω]
(2.) Then did:
I = V/Z = (311∠0) / (3.27∠31.26) = 94.94∠-31.26 [A]
Does the phasor look correct, and can I back into the instantaneous from the phasor?
Thanks for any help! I'm just getting back into this and I'm pretty rusty!