In a certain type of electric generator there is a rotating wire contour connected to the output. The contour is rotating in a magnetic field created by a permanent magnet changing the mechanical work to electrical energy. An electrical lamp was connected to such a generator as an energy consumer. Initially the generator was rotating with an angular velocity ω0 which caused a power P0 to emit from the lamp. At a certain moment the speed of rotation was increased by 2 times.
a) How big was the power emitted from the lamp after increasing the speed of rotation?
b) How big was the torque necessary to rotate the generator before and after changing the speed of rotation?
You can assume that the generator worked without any losses meaning that all the work done by the rotation was transferred to the lamp. When the speed of the rotation is even the torque causing the rotation of the generator is constant. You can also assume that the power of the lamp does not depend on the strength of the current going through it.