# Ohm's Law and Reluctance

## 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 Ohmâ€™s Law. Georg Ohm, a German physicist, published this famous equation in 1827, drawing significant influence from Fourierâ€™s previous work in heat conduction.

Ohmâ€™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 Ohmâ€™s Law, where it is the ratio of the magnetomotive force to the flux, or

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