https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance

Dear Xinyuag,

the Ohmic law is j = sigma*E with j the current density (vector), sigma the conductivity (tensor with generally nine elements and E the electric field (a vector). The electric field determines the potential difference (you call it voltage). The relationship between voltage and field is an integral, in very easy cases V = E*l (l the distance - here a scalarproduct of 2 vectors taking into account the direction of the field and a conductor). In very easy cases the Ohmic law is j = sigma*E and the resistivity is rho = 1/sigma. Nevertheless, generally you must calculate the inverse matrix of sigma, e.g. sigma-1 to get the resistance.

In school you learn V = r*I (r - resistance and 1/r conductance). But this is valid only in isotropic cases.

In more complex cases it could be, that the conductivity itself depends on the voltage (resp. field strength). But this is an effect of higher order.

Yours

R. Mitdank

Conductivity is a constant for any material once it is isotropic in nature. In this case increasing the voltage will simply increase the current. However, at higher voltage conductivity can be dependent on the voltage due to extra effect such as ionization in the medium due to high voltage.