Question

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(1) v

(2) v2

(3) v3

(4) v4

Answer 1

Power output is proportional to the number of molecules striking the blades per unit time (which depends on the velocity, v, of the wind) and also proportional to the energy of striking molecules or proportional to the square of velocity, v2 . therefore, the power output is expressed as

P ∝ v3

Hence, the correct option is (3).