# Energy loss and power over one period?

Let's say we have a ferrite core inductor connected to an AC sinusoidal source with period $T$. Thus, we have voltage $u(t)$ across the inductor and current $i(t)$ through the inductor.
How can we find the equations which describe the power and energy loss due to hysteresis over one period?

We know that power at any point in time is given by: $p(t)=u(t)\cdot i(t)$ and the energy loss over one period is: $$W(T)=\int_T{p(t)dt}$$ But, where do we go from there?

P(t) = u(t) x i(t) is the total loss due to copper resistance, hysteresis and eddy-currents. The hysteresis loss must be calculating using the magnetization curve for the material, the current, number of turns and the material dimensions.

The magnetization curve required would be an AC magnetization curve or hysteresis loop. I believe the hysteresis loop for the specific operating frequency would be required. The material manufacturer would probably provide curves showing core loss per kilogram of material as a function of peak flux density at specific frequencies.

A core manufacturer would probably provide loss information for specific cores.

It may be very difficult to find information that separates hysteresis from eddy-current losses.

• If we take arbitrary dimensions (let's say the core is shaped like a cylinder and has a radius $r$) and there are $N$ turns around the core. The length of the inductor is $l$ and the relative permeability of material is 500, how do we go from here? – A6EE Jan 18 '18 at 18:49
• I revised my answer. The 14 pages that explain core losses in the text book that I have do not really say how to calculate hysteresis loss separate from eddy-current loss. It shows an example calculation using a core loss curve. – Charles Cowie Jan 18 '18 at 19:18