As shown in figure below, the input AC Voltage is vs(t)=320sin(314.159t). The load is highly inductive. It is required to get an average output voltage of 160V, the firing angle alpha in degrees is : Select one:a. 60b. 76.48c. 90d. 38.24
Question
As shown in figure below, the input AC Voltage is vs(t)=320sin(314.159t). The load is highly inductive. It is required to get an average output voltage of 160V, the firing angle alpha in degrees is : Select one:a. 60b. 76.48c. 90d. 38.24
Solution
The average output voltage for a single phase full wave controlled rectifier feeding an inductive load can be given by the formula:
Vavg = (2Vm/π) * (1 + cosα)
Where: Vm is the peak of the input voltage, α is the firing angle.
Given that the input voltage vs(t) = 320sin(314.159t), the peak voltage Vm is 320V.
We are required to find the firing angle α for an average output voltage Vavg of 160V.
Substituting the given values into the formula:
160 = (2*320/π) * (1 + cosα)
Solving the above equation for cosα gives:
cosα = (160π/640) - 1 cosα = 0.5 - 1 cosα = -0.5
Therefore, α = cos^-1(-0.5) = 120 degrees.
However, the firing angle α is defined between 0 and 180 degrees. Therefore, we subtract 120 from 180 to get the correct firing angle.
So, α = 180 - 120 = 60 degrees.
Therefore, the correct answer is a. 60.
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