Power

As one of the roles of a resistor is electrical power dissipation, let us determine the power that is being dissipated when a current is flowing through a resistor. Recall that power is the amount of energy transferred or dissipated per unit time. In the MKS system power has the dimensions of joules per second which is called a watt

.........(1)

Now suppose we have a current flowing through a resistor R as shown in Figure (1). The voltage drop across the resistor is V, from a voltage of V volts at the top to 0 volts at the bottom as shown.
Because V is the electric potential energy of a unit charge (the coulomb), every coulomb of charge flowing through the resistor loses V joules of electric potential energy which is changed to heat. If we have a current i, then i coulombs flow through the resistor every second. Thus the energy lost per second is the number of coulombs (i) times the energy lost per coulomb (V) or (iV):

.........(2)

Ohm’s law, Equation (1), can be used to express the power in terms of R and either i or V

Figure 1: The voltage drops from V to 0 as the current i flows through the resistor. The power dissipated is the current i coulombs/second times the voltage drop V joules/coulomb, which is iV joules/second, or watts.