Mechanical Power is developed by a DC motor

The mechanical power is developed by a DC motor is maximum when

(A) Back emf is equal to twice of applied voltage.

(B) Back emf is equal to half of applied voltage.

(D) None of above.

Answer :-

For motor, E_b = V_t − I_aR_a

Mechanical power developed by the motor is given by P_m = E_bI_a ⇒ V_tI_a − I_a²R_a.

Mechanical power developed by the motor will be maximum if dP_m/dI_a is zero.

i.e. V_t - 2I_aR_a = 0 ⇒ I_aR_a=V_t/2

∴ Back emf E_b = V_t − V_t/2 = V_t/2.

Correct Answer is (B) Back emf is equal to half of applied voltage.