We study the capacity of a uniform G_{\delta} set. Changing the speed at which the lengths of intervals generating it decrease, we observe a sharp phase transition from full to zero capacity. Such a G_{\delta} set is also interesting because it can be considered as a model case for the set of exceptional energies in the parametric version of the Furstenberg theorem. In the talk, we will demonstrate the techniques used and as well as some interesting capacity-related examples.