ABSTRACT: We examine the effect of interactions between the electrons on the Landauer-B\\\"uttiker conductances of some systems of quantum wires with different geometries. The systems include a wire with a stub in the middle, and a wire containing a ring which can enclose a magnetic flux. The electrons in each of the wires is taken to be weakly interacting, and scattering matrices are introduced at all the junctions present in the systems. Using a renormalization group method developed recently, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for high, intermediate and low temperatures which correspond respectively to the thermal coherence length being smaller than, comparable to and larger than the smallest wire length in the different systems, i.e., the length of the stub or each arm of the ring. The renormalization group procedure and the formulae used to compute the conductances are different in the three regimes. Our results show that the Landauer-B\\\"uttiker conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.