Why is there an electric field inside a current-carrying conductor?

[f2009049]

When we connect a battery across a loop of wire having some finite resistance there comes into picture an electric field E which is empirically given by J/sigma.(sigma==>conductivity).
but how can there exist an electric field inside a conductor??We had already learned that electric
conductor inside a conductor is zero.please explain.
(reference griffiths -- electrodynamics)

 

[Doc Al]

We had already learned that electric
conductor inside a conductor is zero.

That's only true for the case of electrostatic equilibrium. When you apply fields and have moving charges, that statement no longer applies.