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A single-phase full-wave controlled rectifier, operating at 120 V rms and 60 Hz ac supply, has a firing angle of 60°. The average value of its output voltage is
  • a)
    52 V
  • b)
    54 V
  • c)
    56 V
  • d)
    58 V
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A single-phase full-wave controlled rectifier, operating at 120 V rms ...
Degrees. The load consists of a resistor and an inductor in series, with R = 10 Ω and L = 0.1 H.

To determine the average output voltage and current, we can use the following steps:

Step 1: Convert the firing angle from degrees to radians.
The firing angle of 60 degrees can be converted to radians using the formula:
Firing angle (radians) = Firing angle (degrees) * (π/180)
Firing angle (radians) = 60 * (π/180) = π/3 radians

Step 2: Calculate the conduction angle.
The conduction angle can be determined by subtracting the firing angle from π radians (180 degrees).
Conduction angle = π radians - Firing angle (radians) = π - π/3 = 2π/3 radians

Step 3: Calculate the average output voltage.
The average output voltage can be calculated using the formula:
Average output voltage = Vrms * (2/π) * (1 - cos(firing angle))
Average output voltage = 120 * (2/π) * (1 - cos(π/3))

Step 4: Calculate the average output current.
The average output current can be calculated using the formula:
Average output current = Average output voltage / Load resistance
Average output current = Average output voltage / R

Step 5: Calculate the ripple factor.
The ripple factor can be determined using the formula:
Ripple factor = (2/π) * (1 - cos(firing angle)) / (1 + cos(firing angle))

Now, let's calculate the values:

Step 1: Convert the firing angle from degrees to radians.
Firing angle (radians) = 60 * (π/180) = π/3 radians

Step 2: Calculate the conduction angle.
Conduction angle = π - π/3 = 2π/3 radians

Step 3: Calculate the average output voltage.
Average output voltage = 120 * (2/π) * (1 - cos(π/3))
Average output voltage ≈ 120 * (2/π) * (1 - 0.5) ≈ 120 * (2/π) * 0.5
Average output voltage ≈ 120 * (1/π) ≈ 120/π ≈ 38.197 V

Step 4: Calculate the average output current.
Average output current = Average output voltage / R
Average output current ≈ 38.197 V / 10 Ω ≈ 3.82 A

Step 5: Calculate the ripple factor.
Ripple factor = (2/π) * (1 - cos(π/3)) / (1 + cos(π/3))
Ripple factor ≈ (2/π) * (1 - 0.5) / (1 + 0.5) ≈ (2/π) * 0.5 / 1.5
Ripple factor ≈ (1/π) / 1.5 ≈ 0.212

Therefore, the average output voltage is approximately 38.197 V, the average output current is approximately 3.82 A, and the ripple factor is approximately 0.212.
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Community Answer
A single-phase full-wave controlled rectifier, operating at 120 V rms ...
Concept:
The average output voltage of the single-phase full-wave rectifier with a resistive load is given by
V0 = 2Vm/π cos α
Where,
Vm = peak value of source voltage
α = firing angle
Calculation:
Given that:
Source voltage Vs = 120 V rms
firing angle α = 600
From the source voltage peak value Vm = √2 × 120 V
The average output value of a single-phase full-wave rectifier is given by
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A single-phase full-wave controlled rectifier, operating at 120 V rms and 60 Hz ac supply, has a firing angle of 60°. The average value of its output voltage isa)52 Vb)54 Vc)56 Vd)58 VCorrect answer is option 'B'. Can you explain this answer?
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