Energy stored in the steady state circuit

[hoangpham4696]

TL;DR Summary: Hi everyone. I have this circuit problem. I know that vL=0 and iL is just a constant number at t-> infiniti. I have attempted this problem and got energy stored = 4.4J. Please confirm it with me if my approach to the problem is correct. Thank you all.

 

[berkeman]

Welcome to PF.

Please confirm it with me if my approach to the problem is correct.

What approach? Please show the work you used to come to that result. Thank you.

 

[hoangpham4696]

Here is my approach

 

[DaveE]

Yes! A good cookbook application of KVL & KCL.
Later, you will learn to do this much more quickly by reducing the complexity of the network with some observations. For example, as you said for steady state $v_l=v_b=0$, so you can replace both of those with a short circuit. That voltage will be zero regardless of the current flow.

 

[hoangpham4696]

Yes! A good cookbook application of KVL & KCL.
Later, you will learn to do this much more quickly by reducing the complexity of the network with some observations. For example, as you said for steady state $v_l=v_b=0$, so you can replace both of those with a short circuit. That voltage will be zero regardless of the current flow.

Thank you so much. I appreciate you checking it for me.

 

[DaveE]

Thank you so much. I appreciate you checking it for me.

Oops! I didn't check the final result. You miscalculated $0.5 LI^2$. You're off by powers of 10. Try that again.

 

[hoangpham4696]

Oops! I didn't check the final result. You miscalculated $0.5 LI^2$. You're off by powers of 10. Try that again.

Ok I see. It should be in nJ. So 4.37 nJ. Thank you

 

[DaveE]

Ok I see. It should be in nJ. So 4.37 nJ. Thank you

Yep. Good work!