What would most likely happen as a result of the generator in a wind turbine breaking?

As a result of the generator in a wind turbine breaking, the electricity would not be produced.  

Generally, the wind turbines work on a very basic phenomenon, here the energy from the wind is used to turn two or three propeller-like blades around a rotor. After this rotor is associated with the main shaft that spins a generator to produce electricity. Therefore, if any of the element of the wind turbine breaks, there will be no electricity produced.  

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