Question

A wind-powered generator converts wind energy into electric 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 proportional to

• A. v
• B. $v^2$
• C. $v^3$
• D. $v^4$

Answer 1

The Correct Option is C

Power = F $\bullet$ v = Fv
$F=v \big(\frac{dm}{dt}\big)=v \Bigg \{ \frac{d(\rho \times \, volume)}{dt}\Bigg \}$
$ \, =\rho v \Bigg \{\frac{d(volume)}{dt}\Bigg \}=\rho v(Av)=\rho Av^2$
$\therefore \, \, \, \, Power \, P=\rho Av^3 \, \, \, \, \, or \, \, \, P = v^3$