Consider a (positive) charge which flows through the battery from the negative
terminal to the positive terminal. The battery raises the potential of the
charge by , so the work the battery does on the charge is .
The total amount of charge which flows through the battery per unit time is,
by definition, equal to the current flowing through the battery. Thus, the
amount of work the battery does per unit time is simply the product of
the work done per unit
charge, , and the charge passing through the battery per unit
time, . In other words,

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This rule does not just apply to batteries. If a current flows through some component of a DC circuit which has a potentialThe power in a DC circuit is the product of the voltage and the current.

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Consider a resistor which carries a current . According to Ohm's
law, the potential drop across the resistor is . Thus, the
energy gained by the resistor per unit time is

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Household electricity bills depend on the amount of electrical
*energy* the household in question uses during a given accounting period,
since the energy usage determines how much coal or gas was burnt on
the household's behalf
in the local power station during this period. The conventional unit of
electrical energy usage employed
by utility companies is the *kilowatthour*. If electrical energy
is consumed for 1 hour at the rate of 1 kW (the typical rate of consumption of
a single-bar electric fire) then the total energy usage is
one kilowatthour (kWh). It follows that

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