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

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) v4 (B) v2 (C) v (D) v3

Tardigrade Admin · Accepted Answer

Power = F bullet v = Fv F=v big((dm/dt) big)=v Bigg (d(ρ × volume)/dt) Bigg =ρ v Bigg (d(volume)/dt) Bigg =ρ v(Av)=ρ Av2 ∴ Power P=ρ Av3 or P = v3

Q. 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

$v^{4}$

$v^{2}$

$v$

$v^{3}$

Power = F $∙$ v = Fv $F = v (\frac{d m}{d t}) = v {\frac{d ( ρ \times v o l u m e )}{d t}}$ $= ρ v {\frac{d ( v o l u m e )}{d t}} = ρ v (A v) = ρ A v^{2}$ $∴ P o w er P = ρ A v^{3} or P = v^{3}$

Q. 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

v4

v2

v

v3

Power = F ∙ v = Fv F=v(dtdm​)=v{dtd(ρ×volume)​} =ρv{dtd(volume)​}=ρv(Av)=ρAv2 ∴PowerP=ρAv3orP=v3

Q. 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

$v^{4}$

$v^{2}$

$v$

$v^{3}$

Power = F $∙$ v = Fv $F = v (\frac{d m}{d t}) = v {\frac{d ( ρ \times v o l u m e )}{d t}}$ $= ρ v {\frac{d ( v o l u m e )}{d t}} = ρ v (A v) = ρ A v^{2}$ $∴ P o w er P = ρ A v^{3} or P = v^{3}$