The resistance of electrons flowing through conductors cause heat. When alloy metals such as Tungsten, Nichrome, Geman silver, brass or bronze are used they heat up quickly. Generally the thicker the wire the less resistance therefore less heat.
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Yes most power stations do use heat to generate electricity. Heat energy of the fuel (e.g. burning coal, burning oil, nuclear fission) is utilized to heat water present in the boiler. This heating generates steam, which is then utilized to run the turbine. However some power stations get the energy to generate electricity without using heat (e.g. hydroelectric dams, wind power, sea wave power, solar cell generation systems).
An ac motor cannot generate electricity but its shaft can be coupled to that of certain devices like an alternator to in order to generate electricity.
When electricity runs through the fillament in a light bulb, the electrons move so fast that they generate heat, which also creates light. Light bulbs actually create more heat than light.
Carbon is a poor conductor of heat and electricity.
Yes, heat and electricity can pass through metals.