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. 72.56 Vb. 269 Vc. 189.99d. 134.54

The RMS (Root Mean Square) value of the output voltage from a half wave controlled rectifier can be calculated using the formula:

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

Where:

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

Given:

• The input voltage v(t) = 300sin(314.159t), so the peak value Vm = 300V
• The firing angle α = 60 degrees = π/3 radians (since 180 degrees = π radians)

Substituting these values into the formula:

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

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

Please note that the power of the resistive load does not affect the RMS value of the output voltage in this case.

Now, let's calculate the above expression:

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

So, the RMS value of the output voltage is approximately 139.59 V. However, this value is not listed in the given options. There might be a mistake in the question or the provided options.