How to Approach an RL Circuit with a Current Source for Homework?

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Discussion Overview

The discussion revolves around solving a homework problem related to an RL circuit with a current source, focusing on the behavior of the circuit before and after a specified time (t=0). Participants explore the application of current divider rules and the implications of inductor behavior in the circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests solving for R1 and R2 for t < 0 but expresses confusion about the approach.
  • Another participant inquires about the equation for current through R2 up until t=0 and how the circuit changes at t=0.
  • A participant proposes a current divider equation but questions whether the resulting fraction is greater than 1.0.
  • There is a discussion about the inductor becoming a current source after the external source is removed, with a mention of exponential decay of energy within the inductor.
  • One participant corrects a previous equation, indicating that the correct form involves Rtotal and R1, and provides the formula for Rtotal.
  • Another participant asks which resistor carries the current, suggesting R2 as the answer.
  • There is a caution against guessing, with a reminder that a more systematic approach is advisable.
  • One participant mentions the relationship between resistance and current flow, indicating a lack of coverage on impedance in their class.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved, particularly regarding the correct application of the current divider and the behavior of the circuit at t=0.

Contextual Notes

Participants express uncertainty about the implications of removing the current source and the behavior of the inductor, as well as the application of impedance in their calculations.

dwn
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Homework Statement



Image


Homework Equations



Current divider

The Attempt at a Solution



The only thing I see is that I solve for R1 and R2 for t < 0. Other than that I'm confused and not even sure I'm right about solving t<0.
 

Attachments

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Up until t=0, what is the equation for current through R2?

How does the circuit change at t=0?
 
Current Divider : 2 ( R1 + R2)/R1

The source is gone, stuck in the closed loop (essentially), and the inductor becomes the current source (the energy within the inductor decays exponentially).
 
dwn said:
Current Divider : 2 ( R1 + R2)/R1
That fraction is > 1.0 ?

The source is gone, stuck in the closed loop (essentially), and the inductor becomes the current source (the energy within the inductor decays exponentially).
So what is the general form of the equation describing this decay?
 
Oh no I'm sorry, it should be 2* ((Rtotal/R1))
Rtotal = (R1*R2)/(R1 + R2)

Ie-Rt/L (R equivalent)
 
dwn said:
Oh no I'm sorry, it should be 2* ((Rtotal/R1))
Rtotal = (R1*R2)/(R1 + R2)
Which resistor carries that current?
 
R2, if I'm not mistaken.
 
dwn said:
R2, if I'm not mistaken.
Guessing is not advisable. Don't you have some way to work it out?
 
Of course, the reason I put that was bc the forum requires min 4 characters...

We choose the "unwanted" resistor to divide from the total because it has something to do with impedance (never covered this topic in class). I know the larger the resistance the less current flowing through it.
 
Last edited:
  • #10
NascentOxygen said:
Guessing is not advisable. Don't you have some way to work it out?

The bread crumbs are not helping.
 

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