Critical field resistance is a term that is associated with a shunt DC generator. In a DC Shunt Generator, the voltage induced across the ArmatureVa is directly proportional to the Flux acting across it, The Flux in a DC Generator is directly proportional to the field current If. By Ohm's LawV = IR . The critical field resistance is defined as the maximum field circuit resistance (for a given speed) with which the shunt generator would excite. The shunt generator will build up voltage only if field circuit resistance is less than critical field resistance.
It is a Tangent to the Open Circuit Characteristics of the Generator(at a given speed).