Question:
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical power output will be most likely proportional to
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical power output will be most likely proportional to
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Kinetic energy of the air swept per second: mass flow rate is \(\rho Av\).
Updated On: Nov 4, 2026
- \(v^4\)
- \(v^2\)
- v
- \(v^3\)
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The Correct Option is D
Solution and Explanation
In time \(t\) the mass of air crossing the blades (area \(A\)) is \(m=\rho A v t\).
Its kinetic energy is \(\frac12mv^2=\frac12\rho Avt\cdot v^2\).
Power in the wind \(=\frac{E}{t}=\frac12\rho Av^3\).
A fixed fraction is converted, so electrical power \(\propto v^3\).
Answer: (4) \(v^3\)
Its kinetic energy is \(\frac12mv^2=\frac12\rho Avt\cdot v^2\).
Power in the wind \(=\frac{E}{t}=\frac12\rho Av^3\).
A fixed fraction is converted, so electrical power \(\propto v^3\).
Answer: (4) \(v^3\)
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