In phase control and Integral cycle control the supply voltage is ac and the armature voltage is rectified ac, where as in chopper control the supply is dc and the average armature voltage is proportional to the duty ratio of the chopper. The chopper system is used for dc traction & battery operated vehicle - Choppers using thyristors are more complicated than the phase control system. This is because an auxiliary commutation arrangement is necessary for choppers, whereas commutation is natural owing to a.c. supply in phase control or integral cycle control. 

Read the paragraph carefully and answer the question based on it.

To determine the displacement factor and power factor of a fully controlled three-phase bridge rectifier without flywheel operation, we need to understand the relationship between the firing angle and these factors.

1. The displacement factor is the cosine of the firing angle \(\alpha\). It represents the phase difference between the input voltage and the fundamental input current. Therefore, the displacement factor is given by:
2. The power factor of the rectifier is affected by the extinction angle, but simplistically, for power factor calculation in rectifiers, we consider the fundamental component of the current. The power factor is the product of the displacement factor and the distortion factor (which comes from the harmonic content of the output current waveform).
3. For a three-phase fully controlled bridge rectifier, the power factor can be expressed as:
4. Considering the given options:
   • Option 1: \(\cos\frac{\alpha}{2}, \sin 2\alpha\) - Incorrect because the forms do not match known formulas for phase control in rectifiers.
   • Option 2: \(\cos\alpha, \frac{3}{\pi}\cos\alpha\) - Correct because this matches the standard formulas for displacement and power factor in fully controlled converters.
   • Option 3: \(\cos(90-\alpha), \cos\alpha\) - Incorrect due to incorrect forms for controlled rectifiers.
   • Option 4: \(\cos 2\alpha, \frac{1}{\pi}\cos 3\alpha\) - Incorrect since these are not standard forms for displacement and power factors.
5. Therefore, the correct answer is:

Understanding these factors is crucial for analyzing the performance of rectifiers in power electronics and drives, especially concerning efficiency and effective control of power.

Step-by-step Solution with Explanation:

In a two-quadrant single-phase SCR drive, the armature current becomes continuous under certain conditions. Let's analyze these conditions step-by-step:

Understanding the Control Method: In phase-controlled rectifiers used in SCR drives, the conduction angle of the SCR determines how much voltage is applied to the motor. The conduction range, referred to as \((\beta - \alpha)\), affects the current characteristics in the circuit.

Continuous Armature Current: Continuous armature current occurs when the SCR remains "on" for a longer duration, allowing continuous current flow through the motor. This typically happens when the conduction angle is large enough to prevent the current from dropping to zero during the non-conduction period.

Evaluating the Options: We need to identify under which condition the armature current remains continuous:

• \(\beta - \alpha\) is equal to or greater than \(180^\circ\): This implies a full or nearly full conduction cycle, leading to continuous current flow.
• \(\beta - \alpha\) is less than \(90^\circ\): This results in very brief conduction periods, leading to discontinuous current.
• \(\beta - \alpha\) is greater than \(90^\circ\) but less than \(120^\circ\): While better than the previous, it still might not ensure continuous current.
• \(\beta - \alpha\) is less than \(45^\circ\): This is too short to sustain continuous current.

Conclusion: The correct condition for continuous armature current in this drive system is when \(\beta - \alpha\) is equal to or greater than \(180^\circ\).

Final Answer: The armature current becomes continuous when \(\beta-\alpha\) is equal to or greater than \(180^\circ\).

To solve this problem, we need to understand the operation of one quadrant converters, particularly in the context of DC motor drives. One quadrant converters, such as half-controlled bridge circuits or single-phase circuits with flywheel diodes, are designed to operate in a single direction of current and voltage. Here’s the detailed explanation:

1. In power electronics, one quadrant operation typically refers to a circuit that allows current and voltage to be positive, meaning power flows in one direction only.
2. The average output voltage being positive means that the current direction and the power flow are both positive, aligning with the motor's natural operation to drive a load in one direction.
3. In these converters, diodes are used to free-wheel the current when the controlled devices (like Thyristors) are not conducting. This ensures that the current remains continuous and the motor continues to receive power, although at a reduced level.
4. The other options can be analyzed as follows:
   • “Average output voltage is always negative” is incorrect because the operation in one quadrant only allows positive voltage and current.
   • “Torque is always negative” is incorrect because, with positive average voltage and current, the motor will produce positive torque in one quadrant operation.
   • “Regeneration is always possible” is incorrect because, in one quadrant converters, regeneration (where the motor acts as a generator and sends power back to the source) is not possible, as the operation is limited to one quadrant.
5. Hence, the most appropriate and correct answer is: "Average output voltage is always positive". This ensures the motor operates in a forward direction, providing positive torque.

Therefore, the correct answer to the question is: Average output voltage is always positive.

The question is about designing a filter for a chopper in a DC drive. The filter should be designed such that the chopper's operating frequency should be at least a certain factor of the resonant frequency. Let's analyze the correct answer.

Concept Explanation:

In a chopper circuit, which is used for converting DC voltage levels, the effective operation depends greatly on the proper filtering of high-frequency components to avoid noise and ripple in the output. This makes the choice of operating frequency critical. The resonant frequency of a filter circuit is given by the formula:

\(\omega_0 = \frac{1}{\sqrt{LC}}\)

where:

• \(L\) is the inductance,
• \(C\) is the capacitance.

The operating frequency of the chopper must be sufficiently higher than the resonant frequency to ensure that the chopper's switching harmonics do not interfere substantially with the filtering process. This is vital because the filter's effectiveness increases with the operating frequency relative to the resonant frequency.

Answer Analysis:

1. 2 times resonant frequency: This is often not sufficient to ensure high-frequency harmonics are filtered effectively.
2. \(\frac{1}{2}\) times resonant frequency: This would result in operating below the resonant frequency, which is not desirable.
3. 4 times resonant frequency: Operating at 4 times the resonant frequency is generally recommended to minimize the impact of switching harmonics and ensure effective filtering. This matches the standard design guidelines.
4. Same as resonant frequency: This doesn't provide a sufficient frequency offset to filter out higher frequency harmonics effectively.

Thus, based on typical design practices and the need for effective harmonic filtering, the correct answer is:

4 times resonant frequency

This ensures the chopper operates well above the resonant frequency, allowing the filter to perform effectively by reducing high-frequency noise and ripples from the chopper output.

The question is about changing the direction of a DC motor in a single quadrant chopper. The correct answer is to change the field, which affects the direction of rotation of the motor.

A single quadrant chopper is a type of DC-DC converter that only allows operation in one of the four quadrants of the speed-torque space. Typically, it facilitates motoring operation, where the motor rotates in a single direction and operates as a load.

1. Changing the Field: The direction of a DC motor can be reversed by changing the direction of either the armature current or the field current. In practical applications, it is more common to change the field current direction since it requires less power and minimizes sparking in the armature.
2. Explanation of Incorrect Options:
   • By changing the direction of the freewheeling diode: This does not affect the motor's direction. A freewheeling diode allows the current to continue flowing through the inductive load when the switch is turned off, helping to prevent voltage spikes.
   • By changing the chopper frequency: The frequency of the chopper influences the switching characteristics and efficiency but does not change the direction of motor rotation.
   • By applying a filter: Filters are used to smooth out voltage or current ripples but do not affect the motor's direction.
3. Conclusion: To reverse the direction of a DC motor in a system using a single quadrant chopper, the field current direction should be changed.

Therefore, the most appropriate way to reverse the direction of a DC motor in a single quadrant chopper is by changing the field.