Wind Energy Conversion

Wind-powered generators are devices that convert wind energy into electrical energy. They typically consist of a rotor with blades, a generator, and various other components. The rotor blades capture the kinetic energy of the wind and transfer it to the generator, where it is converted into electrical energy.

Proportional to Wind Speed

The electrical power output of a wind-powered generator is proportional to the wind speed. This means that as the wind speed increases, the power output of the generator also increases. The relationship between wind speed and power output can be expressed as a mathematical equation. Let's explore the options provided to determine the correct relationship.

a) v
b) v^2
c) v^3
d) v^4

Exploring the Options

a) v: If the power output is proportional to the wind speed (v), it means that doubling the wind speed will double the power output. However, this is not consistent with how wind-powered generators actually work.

b) v^2: If the power output is proportional to the square of the wind speed (v^2), it means that doubling the wind speed will quadruple the power output. This is closer to reality, as wind-powered generators do exhibit a quadratic relationship between wind speed and power output. However, it is not the correct answer.

c) v^3: If the power output is proportional to the cube of the wind speed (v^3), it means that doubling the wind speed will increase the power output by a factor of eight. This is a more accurate representation of the relationship between wind speed and power output for wind-powered generators. Therefore, option 'C' is the correct answer.

d) v^4: If the power output is proportional to the fourth power of the wind speed (v^4), it means that doubling the wind speed will increase the power output by a factor of sixteen. While this relationship may hold true for certain physical phenomena, it does not accurately describe the behavior of wind-powered generators.

Conclusion

In conclusion, the electrical power output of a wind-powered generator is proportional to the cube of the wind speed (v^3). This means that as the wind speed increases, the power output of the generator increases exponentially. Option 'C' is the correct answer in this case.