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. 134.54b. 269 Vc. 189.99d. 72.56 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. 134.54b. 269 Vc. 189.99d. 72.56 V
Solution
The RMS (Root Mean Square) 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 sine function, the coefficient of the sine function is the peak value)
- alpha = 60 degrees = 60 * pi/180 = pi/3 radians (since 1 radian = 180/pi degrees)
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 RMS value of the output voltage is approximately 139.59V. However, this value is not in the given options. There might be a mistake in the problem or the options.
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