Hi Professor, I think for the B-H curve the area between the curve and B axis will determine the energy stored. And for the L-I curve, we need to calculate the integral of L(I)*I*dI, that graphically we should first draw the L(I)*I curve, that will always start from zero and increases with a degree of between one and 2, then we can measure the area between the obtained curve and the I-axis.
I think intuitively that the energy will be L1I1^2/2 eventually, where L1 is inductance at I1. When the inductance is decreasing it means that voltage drop EMF on inductance will decrease(resistance to current change will decrease) and rate of current change will be increased. We can make another experiment where we use bifiliar coil in such a way that most magnetic field is compensated(winding connected in opposing way), and then at some moment we can short one of the windings which will increase the inductance and will cause current drop, since the inductance suddenly will increase.
Thanls for participating. Sorry but not so. As you charge the inductor the energy stored in it is icreasing but LI^2/2 could be decreasing. So L1*I1^2 cannot express the energy stored
@@sambenyaakov But the current should be incresing accordingly in order to keep energy level. So we cannot asume that inductence with value L1 and current I1 has energy of L1I1^2/2. Anyway I will wait for analitical answer thank you.
I think we should refer to energy increment determination. dw=H*dB or dW=I*dФ. Then incremental inductance L=dФ/dI will result in energy stored: W=integrate from 0 to I1 of L(I)*I*dI. Thank you for the video!
@@sambenyaakov We might multiply L(I) curve by line L(I)=I and then take an area of this multiplication. The curve will look like bump, so the energy seems limited. But I think energy will still increase with a current because air inductance is still present even with saturation.
i agree with this, remember the dualities between inductor and capacitor. There have been applications of integral in determining equivalent capacitances of non-linear capacitors, it can be applied to inductor as well IMO. Also qualitatively, note how magnetic flux establish within the core. When the flux increase from zero to saturation, the effective inductance is somewhat high and constant (assume linear BH loop). Beyond the saturation point, effective inductance reduce to air-core value. I would do something similar to what Zaikin proposed: integrate [ L(i) x i x di ] from I1 to I2, where L(i) represent the non-linear inductance across a wide range of bias current. Due to the non-linearity, this should be calculated with numerical methods.
@@sambenyaakov May be we can just get an average value of "μ*μ₀" on interval from 0 to I₁, that will be B₁/H₁ and then plug it into formula I wrote? Then it will turn into W = V * B₁ * H₁ / 2
