When a voltage source raises the electric potential of mobile charge carriers at its terminals, it creates an electric field and this creates a coulomb force on the electrons in the circuit's conductors (wires, connectors, etc) and they are accelerated. When moving through the circuit, these electrons hit atoms and other electrons. These collisions slow down the electrons and raise the temperature of the atoms. The slowing down is resistance and the rise in temperature is a conversion from potential energy to heat.
The power dissipated by a resistor is given by:
P = IV
Since I is CS-1 and V is JC-1, P is JS-1 which is watts.
Fischer-Cripps. A.C., The Electronics Companion. Institute of Physics, 2005.
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