**Equivalent Circuit of a DC Machine**

A review of the material presented with regard to elementary direct-current machines can be helpful at this stage to recall the principles of operation for dc machines. The circuit representations of a dc generator and a dc motor are shown in Figure. Under steady-state conditions the interrelationships between voltage and current are given by

where the plus sign signifies a motor and the minus sign a generator. V_{f} is the voltage applied to the field circuit, If is the field current, and Rf is the field-winding resistance. V_{t} is the terminal voltage, E_{a} is the generated emf, Ia is the armature current, and Ra is the armature resistance. The generated emf E_{a} is given by Equation as

E_{a} = K_{a}φω_{m}

which is the speed (motional) voltage induced in the armature circuit due to the flux of the stator-field current. The electromagnetic torque T_{e} is given by Equation as

T_{e} = K_{a}φI_{a}

where K_{a} is the design constant. The product E_{a}I_{a}, known as the electromagnetic power being converted, is related to the electromagnetic torque by the relation

P_{em} = E_{a}I_{a} = T_{e}ω_{m}

For amotor, the terminal voltage is always greater than the generated emf, and the electromagnetic torque produces rotation against a load. For a generator, the terminal voltage is less than the generated emf, and the electromagnetic torque opposes that applied to the shaft by the prime mover.