Question

A synchronous motor has an equivalent armature reactance of 3.3 Ω.The field current is adjusted so that the induced emf is 950V. If the motor is taking 80 Kw from the supply at 800V, determine the power factor at which the machine operates. 

Answer 1

$$P_m=\frac{E_bV}{X_s}\sin{\alpha}\\80000=\frac{950(800)}{3.3}\sin{\alpha}\\\sin{\alpha}=0.3474\\PF=\cos (\arcsin 0.3474)=0.9377$$