n a certain application, a Half wave controlled rectifier is fed from a voltage vs(t)=320sin(100pi (t)) as shown in figure with an inductive load and a free-wheeling diode. The thyristor firing angle is 90 degrees. Therefore the average output voltage in Volts across the load is: Select one:a. 41.12b. 50.93c. 106.67d. 88.86

The average output voltage (Vavg) for a half-wave controlled rectifier with a firing angle (α) can be calculated using the following formula:

Vavg = (2Vm/π) * (1 + cosα)

Where:

• Vm is the peak voltage, which is 320V in this case.
• α is the firing angle, which is 90 degrees in this case.

First, convert the firing angle from degrees to radians because the trigonometric function in the formula uses radians.

90 degrees = 90 * (π/180) = π/2 radians

Then, substitute the values into the formula:

Vavg = (2*320/π) * (1 + cos(π/2))

Since cos(π/2) = 0, the formula simplifies to:

Vavg = (2*320/π) * 1 = 203.64V

However, this is the average voltage for the full cycle. Since we are dealing with a half-wave rectifier, we only get output for half of the cycle. Therefore, the average output voltage across the load is half of 203.64V, which is approximately 101.82V.

None of the options (a. 41.12, b. 50.93, c. 106.67, d. 88.86) match this result. There might be a mistake in the question or the provided options.