We develop a general formulation of the problem of elastic transport b
etween two semi-infinite systems, connected by a system of finite size
, and derive expressions for the current in and the differential condu
ctance of such a circuit in the limit of zero interactions between the
carriers. These expressions are exact in the applied voltage, the cou
pling of the components of the circuit, and the temperature of the cir
cuit. We then apply our results in a tight-binding approximation to th
ree specific cases: the one-atom contact, the finite, disordered one-d
imensional chain, and the generalized stacking fault.