Complex Notation - Electrical Circuit

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amy1983
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Homework Statement



1 (a) using complex notation, find an expression for the output voltage, v0
1 (b) using complex notation, find an expression for the input current, ig, and hence determine the phase angle of ig relative to vg


Homework Equations





The Attempt at a Solution


See attached two attempts, in jpgs. I've gotten myself very confused! If someone could advise that would be great.
 
Attachments
  • Handwritten circuit solution on lined paper: a source vg = 40 sin(5000t) in series with a 30 ohm resistor and a 1.2 mH inductor in parallel branch, with Figure 1 labelled; working shows jwL = j50, Vr = 40 ∠0 × 30, and the phase angle arctan(2000/1200) = 59 degrees, plus a phasor diagram with 1200 + j2000 and magnitude 2332.39 A.
    Possible Solution 1.jpg
    29.9 KB · Views: 529
  • Handwritten working on lined paper for a circuit problem Q1(a) and Q1(b): a circuit schematic with a source, resistors and a capacitor, followed by complex impedance and current calculations ending in I = -21.35 + j0.856 and phase -2.3 degrees.
    Possible Solution 2.jpg
    25.6 KB · Views: 549
1.2 mH is not the same as 0.001 H; you've dropped a significant figure. This in turn has significantly altered your impedance value for the inductor, with the error propagating through your further calculations.

The input is specified as a voltage source, and you've treated it as a current. This is not correct.

You've then assumed that both the resistor and the inductor are conducting the entire "current" of 40A. They are in parallel so this is not possible; Parallel branches have the same potential difference, but not necessarily the same current. It's series components that have the same current.
 
Thank you gneill, i'll have to look at it and perhaps get a physics tutor.