A wind-powered generator converts wind energy into electrical ene… - Vidyadip

MCQ

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
$v^4$
B
$v^2$
C
$v$
✓
$v^3$

✓

Answer

Correct option: D.

$v^3$

d
Power $=\mathrm{F} \bullet \mathrm{v}=\mathrm{Fv} F=v\left(\frac{d m}{d t}\right)=v\left\{\frac{d(\rho \times \text {volume})}{d t}\right\}$

$=\rho v\left\{\frac{d(v o l u m e)}{d t}\right\}=\rho v(A v)=\rho A v^{2} \therefore$ Power $P=\rho A v^{3} \quad$ or $P=v^{3}$

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