A 220 V, 10 kW, 900 rpm separately excited DC motor has armature resistance 0.02 Ω. At rated speed and voltage it develops electromagnetic torque 70 N·m. Neglect rotational losses. Current drawn from the 220 V supply is
Mechanical converted power is $T\omega=70(900\cdot2\pi/60)=6597.34$ W. This equals back-emf power EI, with $E=220-0.02I$.
Solve $220I-0.02I^2=6597.34$. The normal motor operating root is about 30.07 A; the very large other algebraic root is incompatible with the stated normal rated-speed operation.
The closest listed value is **30 A, B**. The 10 kW rating is not the output being developed at the stated 70 N·m torque.
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