28.3.2 Kilowatt Hours

The energy dissipated (i.e., transformed into thermal energy) by a resistor during time $\text{Δ}t$ is $E_{\text{th}}=P_{\text{R}}\text{Δ}t$. The product of watts and seconds is joules, the SI unit of energy. However, your local electric company prefers to use a different unit, the kilowatt hour, to measure the energy you use each month.

A load that consumes $P_{\text{R}}$ kW of electricity for $\text{Δ}t$ hours has used $P_{\text{R}}\text{Δ}t$ kilowatt hours of energy, abbreviated kWh. For example, a 4000 W electric water heater uses 40 kWh of energy in 10 hours. A 1500 W hair dryer uses 0.25 kWh of energy in 10 minutes. Despite the rather unusual name, a kilowatt hour is a unit of energy. A homework problem will let you find the conversion factor from kilowatt hours to joules.

Your monthly electric bill specifies the number of kilowatt hours you used last month. This is the amount of energy that the electric company delivered to you, via an electric current, and that you transformed into light and thermal energy inside your home. The cost of electricity varies throughout the country, but the average cost of electricity in the United States is approximately $15\text{¢}$ per kWh $(\$0.15\text{/}\text{kWh})$. Thus it costs about $6.00 to run your water heater for 10 hours, about $4\text{¢}$ to dry your hair.