DC Shunt motor problem A 20 hp 250 V shunt motor has an arma

DC Shunt motor problem:

A 20 hp, 250 V shunt motor has an armature circuit resistance of 0.22 Ohm. At no load, the speed is 1200 rpm and the armature current is 3.0 A. At full load and rated voltage, the line current is 55 A. and the flux is reduced by 6% from its values at no load due to armature reaction. What is the full load speed?

Solution

E_no-load=V-I_aR_a =250-3*0.22 =249.34V

I_f =V/R_f =250/170 =1.47A

at full load I_a=I-I_f=55-1.47 =53.53A

E_fullload =250-53.53*0.22 =238.2 V

since speed N proportional to (E/)

N_fullload =1200(238.2/249.34)(1/(1-0.06))

N_fullload =1219.7 rpm 1220rpm