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A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.
- a)1.8
- b)2
Correct answer is between '1.8,2'. Can you explain this answer?
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A single-phase transformer with secondary voltage of 230 V, 50 Hz, de...
The answer is in between 1.8 and 2
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The average value of output voltage is
firing angle = 180∘−120∘=60∘
RMS value of output voltage
Form factor = 
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A single-phase transformer with secondary voltage of 230 V, 50 Hz, de...
The form factor of an alternating current waveform is defined as the ratio of the RMS value to the average value of the waveform. In the case of a half wave-controlled rectifier, the output waveform is a series of half cycles with a firing angle that determines when the rectification occurs.
To find the form factor, we need to calculate the RMS value and average value of the output waveform. First, let's calculate the RMS value.
RMS Value:
The RMS value can be calculated using the formula:
\[V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}\]
where \(V_{\text{max}}\) is the peak value of the output waveform.
In this case, the secondary voltage of the transformer is given as 230 V. Since we are using a half wave-controlled rectifier, the peak value of the output waveform will be equal to the secondary voltage. Therefore, \(V_{\text{max}} = 230\, \text{V}\).
Plugging in the values into the formula, we get:
\[V_{\text{rms}} = \frac{230}{\sqrt{2}}\, \text{V} \approx 162.64\, \text{V}\]
Average Value:
The average value of a half wave rectified waveform can be calculated as:
\[V_{\text{avg}} = \frac{2}{\pi} \cdot V_{\text{max}} \cdot \sin(\alpha)\]
where \(\alpha\) is the firing angle.
In this case, the firing angle is given as 120°. Plugging in the values into the formula, we get:
\[V_{\text{avg}} = \frac{2}{\pi} \cdot 230 \cdot \sin(120°) \approx 261.75\, \text{V}\]
Form Factor:
The form factor can now be calculated as the ratio of the RMS value to the average value:
\[ \text{Form Factor} = \frac{V_{\text{rms}}}{V_{\text{avg}}} \approx \frac{162.64}{261.75} \approx 0.62\]
This value does not match either of the given options (1.8 or 2). It is possible that there may be an error in the question or answer options provided.
Please note that the calculations above assume an ideal rectifier circuit and do not take into account any losses or non-idealities.
To find the form factor, we need to calculate the RMS value and average value of the output waveform. First, let's calculate the RMS value.
RMS Value:
The RMS value can be calculated using the formula:
\[V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}\]
where \(V_{\text{max}}\) is the peak value of the output waveform.
In this case, the secondary voltage of the transformer is given as 230 V. Since we are using a half wave-controlled rectifier, the peak value of the output waveform will be equal to the secondary voltage. Therefore, \(V_{\text{max}} = 230\, \text{V}\).
Plugging in the values into the formula, we get:
\[V_{\text{rms}} = \frac{230}{\sqrt{2}}\, \text{V} \approx 162.64\, \text{V}\]
Average Value:
The average value of a half wave rectified waveform can be calculated as:
\[V_{\text{avg}} = \frac{2}{\pi} \cdot V_{\text{max}} \cdot \sin(\alpha)\]
where \(\alpha\) is the firing angle.
In this case, the firing angle is given as 120°. Plugging in the values into the formula, we get:
\[V_{\text{avg}} = \frac{2}{\pi} \cdot 230 \cdot \sin(120°) \approx 261.75\, \text{V}\]
Form Factor:
The form factor can now be calculated as the ratio of the RMS value to the average value:
\[ \text{Form Factor} = \frac{V_{\text{rms}}}{V_{\text{avg}}} \approx \frac{162.64}{261.75} \approx 0.62\]
This value does not match either of the given options (1.8 or 2). It is possible that there may be an error in the question or answer options provided.
Please note that the calculations above assume an ideal rectifier circuit and do not take into account any losses or non-idealities.
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A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer?
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A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer?.
A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase transformer with secondary voltage of 230 V, 50 Hz, delivers power to a resistive load of 15 Ω through a half wave-controlled rectifier circuit. For a firing advance angle of 120°, then the form factor is _________.a)1.8b)2Correct answer is between '1.8,2'. Can you explain this answer?.
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