How Does Energy Increase in an RL Circuit with Time-Varying Current?

AI Thread Summary
The discussion revolves around calculating the increase in energy stored in an inductor as the current changes from 3 A to 5 A over 1 second. The voltage across the inductor during this time is 4 μV. Participants suggest using the formula U=1/2 I^2L to find the energy, emphasizing the need to first determine the inductance (L) using a derivative-based formula. The conversation highlights the relationship between voltage, current change rate, and inductance in understanding energy dynamics in an RL circuit. The final energy increase calculated is 16 μJ.
syhpui2
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Homework Statement



An inductor initially has 3 A of current passing through it at time t = 0. The current through the inductor increases at a constant rate until 5 A of current is flowing through it 1s later at t = 1 s. The voltage across the inductor is 4 μV while the current is increasing. What is the increase in the energy stored in the inductor between t = 0 and t = 1 s?

Answer: 16 μJ


Homework Equations



KVL, KCL

The Attempt at a Solution



I can use U=1/2 I^2L to find the energy? But how energy increased? And how can I find current over inductor?

Thx
 
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syhpui2 said:
I can use U=1/2 I^2L to find the energy? But how energy increased? And how can I find current over inductor?

Thx

I suggest that you find the inductance L first. What's the defining formula for inductance (hint: it involves a derivative).

Once you have the inductance you can determine the energy stored for each level of current.
 
gneill said:
I suggest that you find the inductance L first. What's the defining formula for inductance (hint: it involves a derivative).

Once you have the inductance you can determine the energy stored for each level of current.

So I just use V/ (dl/dt)?
 
syhpui2 said:
So I just use V/ (dl/dt)?

Try it and find out!
 
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