Help understanding phasor solution

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Discussion Overview

The discussion revolves around understanding a phasor solution related to a circuit homework problem involving inductance, current relationships, and phasor diagrams. Participants are attempting to clarify the drawing of phasors and the implications of circuit parameters on current behavior.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how the phasor for the current ##I_c## is oriented and the reasoning behind the ##I_c/2## representation.
  • Another participant explains that if the inductor were ideal (with R=0), then ##I_c## would lead the current ##I## by 180°, while if the inductance were zero, ##I_c## would lead ##I## by 90°.
  • A participant challenges the previous claim, asserting that ##I## is the inductor current and that ##I_c## would lead the voltage ##U_{12}## by 90°, meaning ##I## lags behind ##U_{12}## by 90° and thus ##I_c## leads ##I## by 180°.
  • Another participant suggests a potential flaw in the question, proposing that the given angular frequency may be too high, which could affect the current magnitudes in the circuit.
  • This participant notes that with a capacitor reactance of 10 Ω and a real resistance of 100 Ω, it may be impossible for the current to match the source current magnitude, even considering resonance effects.

Areas of Agreement / Disagreement

Participants express differing views on the relationships between the currents and the implications of circuit parameters. There is no consensus on the correctness of the phasor orientations or the validity of the problem as posed.

Contextual Notes

Participants highlight potential limitations in the problem setup, including assumptions about ideal components and the specific values of circuit parameters that may affect the analysis.

doktorwho
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Homework Statement


From the given circuit and provided information draw a phasor and calculate the inductance.
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Homework Equations


3. The Attempt at a Solution
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The paper was given to me at class as a solution to our homework and i can't understand how they drew the phasor and drew the conclusion out of it.
I see that they took ##U_{12}## as their phasor axis since its the same for both sides but why do they draw the ##I_c## the way they did? How did they know that it goes up and how did they get the ##I_c/2## part?
The continuation of the left side of the third equation i do get but not the right side. Why is the right side like that?
 
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If the inductor were ideal (with R=0) then IC would lead I by 180°. If the inductance were zero, making it a simple parallel RC arrangement, then IC would lead I by 90°. So with both R and L then IC will lead I by some angle between those 2 extremes. That constrains the shape of triangle that you draw.

You also need to bring into the geometry the condition stated in your data of 2 currents having equal magnitude, viz., I = Ig
 
NascentOxygen said:
If the inductor were ideal (with R=0) then IC would lead I by 180°. g
Do you mean 90° ?
 
Numbskull said:
Do you mean 90° ?
No. I is the inductor current. Ic would lead U12 by 90° and if the inductor were ideal, inductor current I would lag behind U12 by 90°. This means Ic would lead I by 180°.
 
I believe that there is a flaw in the question as posed. Perhaps the angular frequency given is to high? If it is truly ##10^7 rad/sec## then the capacitor reactance is just 10 Ω. The real resistance of 100 Ω in the other branch will make it impossible for it to conduct a current with the same magnitude as the source current, even taking into account resonance effects. If I'm not mistaken the maximum magnitude for the current ##I## would be just 1 mA.
 

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