Finding currents in an LC circuit

[Schfra]

Homework Statement

An image of the problem is attached. I have to find 2 currents in an LC circuit.

Homework Equations

V = L(di/dt)

The Attempt at a Solution

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I have no clue how to do this type of problem. Are there any examples problems similar to this online? Or can someone give me the necessary information to solve the problem. I’m not looking for anyone to solve the problem for me, I’m just looking for somewhere to start.

 

[gneill]

You've only two recourses, Kirchhoff's laws and differential equations, or Laplace transforms to do the "differential stuff" algebraically. Personally I'd choose the Laplace route.

 

[Schfra]

You've only two recourses, Kirchhoff's laws and differential equations, or Laplace transforms to do the "differential stuff" algebraically. Personally I'd choose the Laplace route.

What’s the process for solving a problem like this though? This is the first RL circuit problem I’ve been assigned to do so I’m pretty lost.

I assume I can replace the two inductors on the right with one inductor with a value of 2/3H.

After that, I have no idea what to do. The closest thing I’ve seen to this problem online was a video of someone solving for the current as a function of time before a switch was closed. In this problem, they seem to want current after the switch is opened.

 

[gneill]

I assume I can replace the two inductors on the right with one inductor with a value of 2/3H.

Sure. Might as well incorporate the 3 H inductor as well.

After that, I have no idea what to do. The closest thing I’ve seen to this problem online was a video of someone solving for the current as a function of time before a switch was closed. In this problem, they seem to want current after the switch is opened.

Find the steady state conditions for the circuit before the switch is opened. When the switch opens you've got an RL series circuit with an initial current.

 

[Schfra]

Sure. Might as well incorporate the 3 H inductor as well.

Find the steady state conditions for the circuit before the switch is opened. When the switch opens you've got an RL series circuit with an initial current.

For steady state, I believe I have to treat inductors as short circuits.

I’ve simplified the circuit and then used current division and got a current of 55/23A through the inductor. If I did that right, I think this should be the initial current. What would I then do with that to get current as a function of time?

 

[gneill]

Re-check your current calculation.

What does the part of the circuit of interest look like when the switch opens? Can it be simplified?

 

[Schfra]

Re-check your current calculation.

What does the part of the circuit of interest look like when the switch opens? Can it be simplified?

I re-did the calculation and got 60/23 or about 2.61 for the current through the inductor.

Would the new circuit just be an inductor of 11/3H in series with a resistor of 5 Ohms?

 

[gneill]

I re-did the calculation and got 60/23 or about 2.61 for the current through the inductor.

Would the new circuit just be an inductor of 11/3H in series with a resistor of 5 Ohms?

Yes and yes. What are the initial conditions (the instant following switch opening)? What have you learned about the behavior of an RL circuit?

 

[Schfra]

Yes and yes. What are the initial conditions (the instant following switch opening)? What have you learned about the behavior of an RL circuit?

Looking through my notes I found the equation i(t) = i(0)e^(-(R/L)t), which gives me an answer of i(t) = 60/23e^(-15t/11) for the current through the inductor and -60/23e^(-15t/11) through the resistor. I’m not sure if that’s what you meant by initial conditions, or if my answers are correct.

 

[gneill]

Yes, and your results look good. Be sure to indicate the units (amps) when you submit your results.

 

[Schfra]

Yes, and your results look good. Be sure to indicate the units (amps) when you submit your results.

Alright, thanks for the help.