You are subscribed to this thread L di/dt vs. i dL/dt kmarinas86

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In summary, the conversation discusses the relationship between "L di/dt" and "i dL/dt" in the calculation of inductive reactive power. The concern is whether the convention of only considering "L di/dt" is accurate and if there is a need to also include the term "i dL/dt" in the calculation. It is suggested that the complete derivative of (1/2)Li^2 may be a more accurate representation of inductive reactive power. However, there is no known peer-reviewed source to support this concern. Additionally, it is noted that changes in inductance and current can both affect the energy stored in a magnetic field.
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kmarinas86
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"L di/dt" vs. "i dL/dt"

I have heard many times that the positive "inductive" part of a circuit's reactive power is equal to "L i di/dt".

I also know that "L di/dt" is just one of two terms that is derived from applying derivative of "L i" with respect to time. The other term is "i dL/dt".

My concern is the relationship between "L i" and the integration of "L di/dt" with respect to time t. I have heard that "L i" is equal to magnetic flux. However, I know that in cases when L changes over the course of time that it is possible that "L i" to be greater than integration of "L di/dt" with respect to time t.

What if the magnetic circuit is changing such that the inductance of the coil changes with respect to the surrounding and interior (magnetic) permeabilities? Taken to an extreme, if the inductance is increasing and the current is not changing, then it appears that the reactive power "L i di/dt" is still zero. But it seems apparent that the increases of inductance increases the potential energy in the field given the current already there.

Perhaps the problem I have originates from the convention where inductive reactive power is equal to "L i di/dt", ignoring cases where "i dL/dt" is non-zero. Perhaps inductive reactive power is really "L i di/dt + (1/2) i^2 dL/dt". That is the complete derivative of (1/2)Li^2.

Does anyone know of an independent peer-review source that gives credence to my concern?
 
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kmarinas86 said:
Perhaps the problem I have originates from the convention where inductive reactive power is equal to "L i di/dt", ignoring cases where "i dL/dt" is non-zero. Perhaps inductive reactive power is really "L i di/dt + (1/2) i^2 dL/dt". That is the complete derivative of (1/2)Li^2.

Does anyone know of an independent peer-review source that gives credence to my concern?

I'd say your calculation is correct. The power consists of two terms both containing L(t). Thus at any time t the above two terms calculate the instantaneous power. Note that if the current is constant (di/dt =0) then only the second terms contributes. But this makes sense in that an increase of inductace means you are increasing the energy put into the system to increase the inductance which means more energy stored in the magnetic field. That increase shows up as the power represented by the second term. Hence one can store and remove energy from a magnetic field either by an increase or decrease in the current in the inductor and also by changing the physical configuration of the inductor to provide for more or less flux in space. And obviously one can also do both at the same time.

I see no problem worthy of a peer-reviewed source here.
 
  • #3


I would like to address your concerns and provide some clarification on the relationship between "L di/dt" and "i dL/dt". Firstly, it is important to understand that "L di/dt" and "i dL/dt" are both terms derived from the same concept of inductance, but they represent different aspects of it.

"L di/dt" represents the change in current over time, while "i dL/dt" represents the change in inductance over time. Both of these terms are important in understanding the behavior of inductive circuits, as they contribute to the overall reactive power.

To answer your question about the relationship between "L i" and the integration of "L di/dt" over time, it is important to note that "L i" is the product of inductance and current, and it represents the energy stored in the magnetic field of the circuit. On the other hand, the integration of "L di/dt" over time represents the change in this stored energy. Therefore, it is possible for "L i" to be greater than the integration of "L di/dt" if the inductance of the circuit is changing over time.

In the case of a changing magnetic circuit, where the inductance is affected by the surrounding and interior permeabilities, it is important to consider both "L di/dt" and "i dL/dt" in order to fully understand the behavior of the circuit. The reactive power in this case would be equal to "L i di/dt + (1/2) i^2 dL/dt", as you have correctly stated.

As for an independent peer-review source, I suggest looking into textbooks on electromagnetic theory or consulting with experts in the field for further clarification on this topic. It is always important to seek out reliable sources and engage in critical thinking when it comes to understanding scientific concepts.

I hope this helps to address your concerns and provide a better understanding of the relationship between "L di/dt" and "i dL/dt". Remember, as scientists, it is our responsibility to continuously question and seek out knowledge in order to deepen our understanding of the world around us.
 

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