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.

(C)
 Back emf is
equal to 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.