For electrical drives (A) For Tm(t) < TL(t), dω/dt > 0...

 

58) For electrical drives

• (A) For T_m(t) < T_L(t),
  dω/dt
  > 0
• (B) For T_m(t) > T_L(t),
  dω/dt
  > 0, speed increases
• (C) For T_m(t) = T_L(t),
  dω/dt
  = 0, drive attains steady state
• (D) The Equation J
  dωdt
  + B
  dω(t)dt
  = T_m(t) - T_L(t)
• (E) Equation J
  dωdt
  + Bω = T_m(t) - T_L(t)

Choose the correct answer from the options given below :

• (1) (B), (C), (E) only
• (2) (A), (C), (D) only
• (3) (A), (D), (E) only
• (4) (B) and (D) only

Answer: A

Evaluating the Statements:

• (A) For 

  $T_m<T_L,\frac{d\omega }{dt}>0$

  :
  Incorrect. If the "drag" (

  $T_L$

  ) is stronger than the "push" (

  $T_m$

  ), the motor must slow down. Acceleration (

  $\frac{d\omega }{dt}$

  ) would be negative (

  $<0$

  ), not positive.

• (B) For 

  $T_m>T_L,\frac{d\omega }{dt}>0$

  , speed increases:
  Correct. If the "push" is stronger than the "drag," the motor accelerates, and the speed goes up.

• (C) For 

  $T_m=T_L,\frac{d\omega }{dt}=0$

  , drive attains steady state:
  Correct. When the forces are balanced, there is no change in speed. It keeps spinning at a constant rate, which is called "steady state."

• (D) The Equation 

  $J\frac{d\omega }{dt}+B\frac{d\omega (t)}{dt}=T_m-T_L$

  :
  Incorrect. This equation is mathematically weird because it has acceleration in both terms on the left. The friction term (

  $B$

  ) should depend on speed (

  $\omega$

  ), not acceleration.

• (E) Equation 

  $J\frac{d\omega }{dt}+B\omega =T_m-T_L$

  :
  Correct. This is the fundamental equation for motor dynamics. It says: (Net Torque) = (Force to overcome inertia) + (Force to overcome friction).

Conclusion:

Statements (B), (C), and (E) are correct.

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