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A half wave controlled rectifier is used in certain application is connected to an AC Voltage : v(t) = 300sin(314.159t). The RMS value of the output voltage from such a converter at a resistive load of 3kW at a Firing angle of 60 degrees is....Select one:a. 189.99b. 134.54c. 72.56 Vd. 269 V

Question

A half wave controlled rectifier is used in certain application is connected to an AC Voltage : v(t) = 300sin(314.159t). The RMS value of the output voltage from such a converter at a resistive load of 3kW at a Firing angle of 60 degrees is....Select one:a. 189.99b. 134.54c. 72.56 Vd. 269 V

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Solution 1

The RMS value of the output voltage from a half wave controlled rectifier can be calculated using the formula:

Vrms = Vm/2 * sqrt((pi - α + 0.5sin(2α))/pi)

where:

  • Vm is the peak value of the input voltage
  • α is the firing angle in radians

Given:

  • Vm = 300V (since the given voltage v(t) = 300sin(314.159t) is a sine function, the coefficient of the sine function is the peak value)
  • α = 60 degrees = pi/3 radians (since 60 degrees = pi/3 radians)

Substituting these values into the formula, we get:

Vrms = 300/2 * sqrt((pi - pi/3 + 0.5sin(2pi/3))/pi) = 150 * sqrt((2pi/3 + 0.5sin(2*pi/3))/pi)

Calculating the above expression will give us the RMS value of the output voltage.

Let's calculate it:

Vrms = 150 * sqrt((2pi/3 + 0.5sin(2pi/3))/pi) = 150 * sqrt((2.0944 + 0.50.866)/3.1416) = 150 * sqrt(0.866) = 150 * 0.9306 = 139.59 V

So, the closest answer to this value is 134.54 V (option b).

This problem has been solved

Solution 2

The RMS value of the output voltage from a half wave controlled rectifier can be calculated using the following formula:

Vrms = Vm/2 * sqrt((pi - alpha + 0.5sin(2alpha))/pi)

Where:

  • Vm is the peak value of the input voltage
  • alpha is the firing angle in radians

Given:

  • Vm = 300V (since the given voltage v(t) = 300sin(314.159t) is a sinusoidal function, the coefficient of the sine function gives the peak value)
  • alpha = 60 degrees = 60 * pi/180 = pi/3 radians

Substituting these values into the formula gives:

Vrms = 300/2 * sqrt((pi - pi/3 + 0.5sin(2pi/3))/pi) = 134.54V

So, the correct answer is b. 134.54V.

This problem has been solved

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