ELECTRIC GENERATORS
A 120-V generator is run by a windmill that has blades 2.0 m long. The wind, moving at 12 m/s, is slowed to 7.0 m/s after passing the windmill. The density of air is
A 120-V generator is run by a windmill that has blades 2.0 m long. The wind, moving at 12 m/s, is slowed to 7.0 m/s after passing the windmill. The density of air is
The largest current produced by the
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The length of the blade is
Thevoltage of the generator is
The density of air is
The initial speed of the wind is
The final speed of the wind is
Formula used:
The expression of mechanical power is expressed as,
Here,
The expression of electrical power is expressed as,
Here,
The work-energy theorem is expressed as,
Here,
The expression of kinetic energy is expressed as,
Here,
The expression of density of the material is expressed as,
Here,
The volume of cylindrical shape is expressed as,
Here,
Explanation:
Consider the expression of wind power.
Consider the work energy theorem.
Substitute
Understand that the wind comes with speed
Therefore, the expression of wind power can be written as,
Consider the expression of density of air.
Rearrange the expression.
Substitute
Consider the expression of volume.
Substitute
Understand that the
Here,
Substitute
Negative sign indicates that the power is loss.
The magnitude of the power loss of the wind is,
Consider the expression of electrical power.
Understand that there is no loss, hence, this wind power is converted in to the electrical power completely. In this case, the current would be maximum.
Substitute
Substitute
Solve for
Conclusion:
The maximum current that generator can be producedis
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Chapter 33 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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