For a motor with a separate excitation, we obtain the circuit shown in Fig. 224. In the first case, i.e. when the winch is not loaded 0 = I1 = (ξ - ξ1)/r, where r is the internal resistance of the motor, and ξ1 is the induced emf, ξ1 = αv1. Thus, ξ1 = ξ, whence a = ξ/v1. In the second case, the power consumed by the motor is
The induced emf is now ξ2 = αv2. Thus, for the internal resistance of the motor, we obtain
For the maximum liberated power, we can write
where it can easily be shown that the maximum power ξ' = αv' is liberated under the condition
ξ' = ξ/2 (the maximum value of the denominator). Hence
