The effective conductivity eff of a magnetized plasma with random irregularities has been studied theoretically. The main aim of this research is to construct a general theory valid to unbounded (closed Hall circuit) as well as to bounded plasma systems (opened Hall circuit) with one kind of current carrier. Our results reveal essential differences in behaviour of eff in these cases. The behaviour eff following from the theoretical considerations has been confirmed in experiments on thin non-homogeneous plates of crystal p-Si in crossed electric and magnetic fields (from 0 to 15 kGs) placed in liquid He. In the case of an open Hall circuit, eff differs only slightly from the average in the whole range of the magnetic fields. In contrast, eff may be higher than for a closed Hall circuit when the magnetization parameter is greater than 10.