  The conductance steps in a constricted two-dimensional electron gas and the
minimum conductivity in graphene are related to a new uncertainty relation
between electric charge and conductance in a quantized electric circuit that
mimics the electric transport in mesoscopic systems. This uncertainty relation
makes specific use of the discreteness of electric charge. Quantum electric
circuits analogous to both constricted two-dimensional electron gas and
graphene are introduced. In the latter case a new insight into the origin of
minimum conductivity is obtained.
