Wouldn't the generalized law need to work for capacitors (or other current sources and sinks) in order to be general? In those cases, you would need a term with non-vanishing divergence.mertcan said:
Generalized Ohm's Law is an extension of the traditional Ohm's Law, which relates the current flowing through a material to the voltage and resistance. Generalized Ohm's Law includes additional factors such as current density and capacitance, making it more applicable to a wider range of materials and circuits.
Current density is a measure of the amount of electric current flowing through a given area of a material. It is represented by the symbol J and is calculated by dividing the total current by the cross-sectional area of the material.
In Generalized Ohm's Law, capacitance is included as a factor in the equation to account for the storage of electric charge in a material. The higher the capacitance, the more charge a material can hold at a given voltage.
While Ohm's Law is primarily used for conductors, Generalized Ohm's Law can be applied to both conductors and insulators, as it takes into account additional factors such as capacitance and current density.
Generalized Ohm's Law is useful for scientists as it provides a more comprehensive understanding of the relationships between current, voltage, resistance, and other factors in a material or circuit. It allows for more accurate predictions and analysis of electrical systems and can be applied to a wider range of materials and situations.
