For ferroresonant circuits, the sufficient condition for preventing fundamental ferroresonance (FF) from occuring is that there is no intersection between the voltage-current characteristic of the linear part of the circuit, and the saturated power frequency excitation characteristic of the nonlinear part. Based on this understanding, part 11 of this paper has presented a criterion for the possibility of FF in the form of an analytical expression which is composed of the essential parameters of the circuit. By giving the critical resistance value for damping FF, the expression clearly indicates not only the possibility of FF but also the methods for eliminating the FF. The possibility of FF is judged by comparing the critical resistance value with the real value. In the meantime, the expression suggests how to adjust the essential parameters to suppress FF. The criterion has been proven by both simulation results and field tests. With this criterion, the possibility and elimination of FF can be studied for the first time by a simple yet effective analytical method.