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A single-phase transformer, with secondary voltage of 250 V, 50 Hz delivers power to R load of 15 Ω through a half wave-controlled rectifier circuit. For firing angle of 45°, the form factor is____
  • a)
    0.569
  • b)
    1.75
  • c)
    2
  • d)
    0.5
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A single-phase transformer, with secondary voltage of 250 V, 50 Hz de...
Average value of output voltage
RMS value of output voltage,
Vorms =168.55V
Form factor, FF = = 1.75
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Most Upvoted Answer
A single-phase transformer, with secondary voltage of 250 V, 50 Hz de...
Given data:
Secondary voltage, V = 250 V
Frequency, f = 50 Hz
Load resistance, R = 15 Ω
Firing angle, α = 45°

To find: Form factor

Calculation:
The output voltage of the half wave-controlled rectifier is given by:

V_o = V_m/π * (1 - cos α) * sin ωt

where V_m is the peak value of the secondary voltage and ω is the angular frequency.

The RMS value of the output voltage is given by:

V_rms = V_m/π * (1 - cos α) / √2

The average value of the output voltage is given by:

V_avg = 2V_m/π * (1 - cos α) / π

The DC component of the output voltage is given by:

V_DC = V_m/π * (1 - cos α)

The form factor is the ratio of the RMS value to the average value of the output voltage:

Form factor = V_rms / V_avg

Substituting the above equations, we get:

Form factor = √2 / (2/π * (1 - cos α))

Form factor = √2 / (2/π * (1 - cos 45°))

Form factor = √2 / (2/π * (1 - 1/√2))

Form factor = 1.75

Therefore, the form factor is 1.75.

Answer: b) 1.75
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A single-phase transformer, with secondary voltage of 250 V, 50 Hz delivers power to R load of 15 Ω through a half wave-controlled rectifier circuit. For firing angle of 45°, the form factor is____a)0.569b)1.75c)2d)0.5Correct answer is option 'B'. Can you explain this answer?
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