# Energy Stored in An Inductor

#### BlackMelon

Joined Mar 19, 2015
141
Hi there!

I'm working on switching power supplies, and curious about the energy stored in an inductor (U(t) in the attached picture). I would like to ask you guys if this derivation is correct or not? If so, are we good to assume U(t0) = 0?

Sincerely,
BlackMelon

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#### Papabravo

Joined Feb 24, 2006
19,287
The derivation has the correct form, but I see no evidence for the supposition that U(t0) = 0
Since the current seems to be piecewise linear, I would suppose that the current at t0 is not zero, and that is was not zero just before t0. That is at t0 - Δt.
What is wrong with U(t0) being non-zero?
That means, in the last line, you are subtracting the energy at t0 and then adding the same quantity back so you end up with the final result that the energy at a point in time t2 is just:

$\frac{1}{2}L(i(t_2))^{2}$

Do you see it that way or did I miss something?

#### BlackMelon

Joined Mar 19, 2015
141
Most of the textbooks say like the expression you provided. However, I think that the energy depends on the point of reference. For example, like potential energy of a ball thrown upward depends on the reference height.

I am not sure if this would apply to the energy stored in the inductor or not, since the textbook usually gives a formula without much derivation. That's why I am asking here to be sure.

#### Papabravo

Joined Feb 24, 2006
19,287
Most of the textbooks say like the expression you provided. However, I think that the energy depends on the point of reference. For example, like potential energy of a ball thrown upward depends on the reference height.

I am not sure if this would apply to the energy stored in the inductor or not, since the textbook usually gives a formula without much derivation. That's why I am asking here to be sure.
With an inductor you have an absolute reference. With zero current, there is zero energy stored in the magnetic field. Energy is conserved, so whatever current goes into the inductor is converted to energy in the magnetic field. When that energy in the magnetic field is converted back into current, everything is in balance. The result does not depend on the path. It is only a function of the current value.