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

[syhpui2]

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

 

[gneill]

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.

 

[syhpui2]

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)?

 

[gneill]

So I just use V/ (dl/dt)?

Try it and find out!

 

[asteriatic]

for reaching out! I would approach this problem using the equation U=1/2 LI^2 to calculate the energy stored in the inductor. Since the current is increasing at a constant rate, we can use the average value of the current (4 A) to calculate the energy at t=1s, which would be 8 μJ. Similarly, at t=0, the energy stored in the inductor would be 4.5 μJ. Therefore, the increase in energy would be 8 μJ - 4.5 μJ = 3.5 μJ. This is because the energy stored in an inductor is directly proportional to the square of the current passing through it. I hope this helps!