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The electrical time-constant of an armature- controlled dc servomotor is
- a)larger than mechanical time-constant
- b)not related to mechanical time-constant
- c)equal to mechanical time-constant
- d)smaller than mechanical time-constant
Correct answer is option 'D'. Can you explain this answer?
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The electrical time-constant of an armature- controlled dc servomotor ...
Explanation:
Armature-controlled DC servomotors are widely used in various applications such as robotics, automation, and control systems. The electrical time constant of a DC servomotor is an important parameter that determines the response time of the motor to a change in the input signal. The electrical time constant of a motor is defined as the time required for the motor to reach 63.2% of its steady-state speed when subjected to a step change in the input voltage.
The mechanical time constant of a motor is the time required for the motor to reach 63.2% of its steady-state torque when subjected to a step change in the load torque. The mechanical time constant is related to the moment of inertia of the rotor and the load attached to the motor shaft.
The relationship between the electrical and mechanical time constants can be derived from the transfer function of the motor. The transfer function of a DC servomotor is given by:
G(s) = K / (s(Tm*Te) + 1)
where G(s) is the transfer function, K is the motor gain, Tm is the mechanical time constant, and Te is the electrical time constant.
From the transfer function, it can be seen that the electrical time constant is inversely proportional to the product of the mechanical time constant and the electrical time constant. Therefore, the electrical time constant is smaller than the mechanical time constant.
Hence, the correct answer is option D, i.e., the electrical time constant of an armature-controlled DC servomotor is smaller than the mechanical time constant.
Armature-controlled DC servomotors are widely used in various applications such as robotics, automation, and control systems. The electrical time constant of a DC servomotor is an important parameter that determines the response time of the motor to a change in the input signal. The electrical time constant of a motor is defined as the time required for the motor to reach 63.2% of its steady-state speed when subjected to a step change in the input voltage.
The mechanical time constant of a motor is the time required for the motor to reach 63.2% of its steady-state torque when subjected to a step change in the load torque. The mechanical time constant is related to the moment of inertia of the rotor and the load attached to the motor shaft.
The relationship between the electrical and mechanical time constants can be derived from the transfer function of the motor. The transfer function of a DC servomotor is given by:
G(s) = K / (s(Tm*Te) + 1)
where G(s) is the transfer function, K is the motor gain, Tm is the mechanical time constant, and Te is the electrical time constant.
From the transfer function, it can be seen that the electrical time constant is inversely proportional to the product of the mechanical time constant and the electrical time constant. Therefore, the electrical time constant is smaller than the mechanical time constant.
Hence, the correct answer is option D, i.e., the electrical time constant of an armature-controlled DC servomotor is smaller than the mechanical time constant.
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The electrical time-constant of an armature- controlled dc servomotor isa)larger than mechanical time-constantb)not related to mechanical time-constantc)equal to mechanical time-constantd)smaller than mechanical time-constantCorrect answer is option 'D'. Can you explain this answer?
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