RL Circuit with current source

In summary, the conversation discusses the use of a current divider to solve for R1 and R2 for t < 0, and the equation for current through R2 until t=0. It also mentions the change in the circuit at t=0 and the general form of the equation describing the decay. The conversation also touches on the use of the larger resistor in the current divider and the importance of working out the solution instead of just guessing.
  • #1
dwn
165
2

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.
 

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  • #2
Up until t=0, what is the equation for current through R2?

How does the circuit change at t=0?
 
  • #3
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).
 
  • #4
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?
 
  • #5
Oh no I'm sorry, it should be 2* ((Rtotal/R1))
Rtotal = (R1*R2)/(R1 + R2)

Ie-Rt/L (R equivalent)
 
  • #6
dwn said:
Oh no I'm sorry, it should be 2* ((Rtotal/R1))
Rtotal = (R1*R2)/(R1 + R2)
Which resistor carries that current?
 
  • #7
R2, if I'm not mistaken.
 
  • #8
dwn said:
R2, if I'm not mistaken.
Guessing is not advisable. Don't you have some way to work it out?
 
  • #9
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.
 

1. What is an RL circuit with current source?

An RL circuit with current source is an electrical circuit that contains a resistor (R) and an inductor (L) in series, with a constant current source providing a constant flow of current. It is a type of circuit commonly used in electronics and electrical engineering.

2. What is the difference between an RL circuit with current source and an RC circuit with current source?

The main difference between an RL circuit with current source and an RC circuit with current source is the presence of an inductor in the former and a capacitor (C) in the latter. Inductors and capacitors have opposite effects on the flow of current, with inductors resisting changes in current and capacitors allowing current to flow more easily.

3. How does an RL circuit with current source behave over time?

An RL circuit with current source will exhibit transient behavior over time, as the inductor takes time to build up its magnetic field and resist changes in current. This can result in a delay in the response of the circuit to changes in the current source.

4. What is the time constant of an RL circuit with current source?

The time constant of an RL circuit with current source is equal to the ratio of the inductance (L) to the resistance (R) of the circuit. It represents the amount of time it takes for the current in the circuit to reach 63.2% of its maximum value when a constant current source is connected.

5. How can the behavior of an RL circuit with current source be described mathematically?

The behavior of an RL circuit with current source can be described by an equation known as the differential equation of an RL circuit. This equation takes into account the effects of the inductor and resistor on the current in the circuit and can be solved using techniques such as Kirchhoff's laws and Laplace transforms.

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