Source Free RL circuit confusion

[MagnificentLiver]

1. The problem statement, all variables, and given/known data
I have a single loop RL circuit with no source. I am given the the inductance of 3mH, as well as that energy storage is as follows 1 J @ t=0 and 100mJ @ t=1ms. No current is given. I have to find R. I don't need the answer just some ideas of where to start. Thanks!

Homework Equations

The only equations I can think of are p=i(0)^2 * Re-2R/L t , 1/2Li(0)^2, and i=i(0)e-R/L t.

The Attempt at a Solution

I initially got .0015 Ohms (which I know is incorrect)

 

[berkeman]

1. I have a single loop RL circuit with no source. I am given the the inductance of 3mH, as well as that energy storage is as follows 1 J @ t=0 and 100mJ @ t=1ms. No current is given. I have to find R. I don't need the answer just some ideas of where to start. Thanks!2. The only equations I can think of are p=i(0)^2 * Re-2R/L t , 1/2Li(0)^2, and i=i(0)e-R/L t.3. I initially got .0015 Ohms (which I know is incorrect)

Welcome to the PF.

Can you show your calculations that resulted in your answer? That would help a lot to show us your approach.

Also, I don't see the equation in your Relevant Equations section for the energy stored in an inductor in terms of the inductance and the current. Oh, wait, I see the expression, but it's not shown as an equation. Anyway, can you show your work so far? Thanks.

 

[MagnificentLiver]

I used 1/2i_o²L

1J=.5i_o²(3mH)

2J/(3mH)=io²
R=P/i²
R=1/(25.8²)

R=.0015. (I'm sure this I wrong and we haven't covered in our notes how to proceed to my knowledge)

 

[berkeman]

I used 1/2io^2L. 1J=.5io^2(3mH)

2J/(3mH)=io^2 R=P/i^2. R=1/25.8^2

R=.0015. (I'm sure this I wrong and we haven't covered in our notes how to proceed to my knowledge)

It's really hard to try to read your work the way it's typed, but it looks like you are on the right track and trying your best on this. Here is a LaTeX Primer that you should read through to help with your online math and science posts:

https://www.physicsforums.com/help/latexhelp/

Let me try to help with the LaTeX version of what you are trying to do...

The two Relevant Equations that you correctly listed are:
$$E = \frac{1}{2} L I^2$$
$$I(t) = I_0 \exp{-t\frac{R}{L}}$$

Now can you use my example LaTeX and show the two equations for the two energies (that gives you the two currents), and then use the exponential equation with the two currents and times to calculate the resistance?