In a certain application, a Half wave controlled rectifier is fed from a voltage vs(t)=320sin(100pi (t)). The thyristor firing angle is 90 degrees. The conduction angle Beta=210 degrees due to inductive loading. Therefore the average output voltage in Volts across the load is: Select one:a. 44.12b. 51.72c. 103.44d. 88.68

The average output voltage (Vavg) for a half-wave controlled rectifier with inductive load can be calculated using the formula:

Vavg = (Vm/2π) * (1 + cosα)

Where:

• Vm is the peak voltage
• α is the firing angle

Given:

• Vm = 320V (since the given voltage vs(t) = 320sin(100πt), the peak voltage Vm is the amplitude of the sine wave, which is 320V)
• α = 90 degrees

Substituting these values into the formula, we get:

Vavg = (320/2π) * (1 + cos90) = (160/π) * (1 + 0) [since cos90 = 0] = 160/π = 50.92V

However, this is not the final answer because the conduction angle β = 210 degrees is given. The conduction angle is the period during which the thyristor conducts. Since the conduction angle is more than 180 degrees, the thyristor conducts for more than half the time period. Therefore, the average output voltage will be more than 50.92V.

The average output voltage considering the conduction angle is given by:

Vavg = (Vm/2π) * (β - α)

Substituting the given values, we get:

Vavg = (320/2π) * (210 - 90) = (160/π) * 120 = 6111.46V

This value is not in the given options. There seems to be a mistake in the problem or the options provided. Please check the problem statement and the options again.

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

Vavg = (Vm/2π) * (1 + cosα)

Where:

• Vm is the peak voltage
• α is the firing angle

Given:

• Vm = 320V (since the given voltage vs(t) = 320sin(100πt), the peak voltage Vm is the amplitude of the sine wave, which is 320V)
• α = 90 degrees

Substituting these values into the formula, we get:

Vavg = (320/2π) * (1 + cos90) = (160/π) * (1 + 0) [since cos90 = 0] = 160/π = 50.92V

However, this is not the final answer because the conduction angle β = 210 degrees is also given. The conduction angle is the period during which the thyristor conducts. Since the conduction angle is more than 180 degrees, the thyristor conducts for more than half the cycle. Therefore, the average output voltage will be more than what we calculated above.

The exact effect of the conduction angle on the average output voltage depends on the specific circuit configuration and load characteristics, which are not given in the question. Therefore, we cannot calculate the exact average output voltage with the given information.

However, we can say that the average output voltage will be more than 50.92V. Therefore, the correct answer is either option c. 103.44V or option d. 88.68V. Without more information, we cannot determine which one is correct.