Ohm's Law and Reluctance

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Ohm's Law

Electric circuits share many of the same characteristics as magnetic circuits. One of the most important and fundamental equations describing electric circuits is Ohm’s Law. Georg Ohm, a German physicist, published this famous equation in 1827, drawing significant influence from Fourier’s previous work in heat conduction.


Ohm’s Law states that the resistance of a conductor is constant and inversely proportional to the current running through the conductor and directly proportional to the voltage across it, or expressed mathematically as


R=\frac{V}{I}


The SI units for resistance are the Ohm (\Omega), voltage is expressed in volts (V) and current is measured in amperes (A).


Expressed differently, the current density J (A/m^2) is proportional to the product of conductivity sigma (V/m) and the electric field E (siemens/meter, s/m), or


\displaystyle J=\sigma E

Reluctance

Now, consider a material of very high permeability with flux \Phi running through it and separated by a very small gap of area A, where the flux flows through this gap as if it were free space. The flux density crossing this gap is B. Therefore


\displaystyle \Phi=BA


The magnetic field intensity can be approximated by H=\frac{B}{\mu_0}


The reluctance of this gap is analogous to the resistance described by Ohm’s Law, where it is the ratio of the magnetomotive force to the flux, or


\R = \frac{F}{\phi}