An electric heater of resistance 8.0 Ωdraws 15 A from the...

An electric heater of resistance $8.0 \Omega$ draws $15 \mathrm{~A}$ from the service mains. At what rate is thermal energy developed, in W? What is the cost of operating the heater for a period of $4.0 \mathrm{~h}$ at $10 \phi / \mathrm{kW} \cdot \mathrm{h} ?$ $$ \begin{aligned} W &=I^{2} R=(15 \mathrm{~A})^{2}(8.0 \Omega)=1800 \mathrm{~W}=1.8 \mathrm{~kW} \\ \text { Cost } &=(1.8 \mathrm{~kW})(4.0 \mathrm{~h})(10 \& / \mathrm{kW} \cdot \mathrm{h})=72 \epsilon \end{aligned} $$

An electric heater of resistance $8.0 \Omega$ draws $15 \mathrm{~A}$ from the service mains. At what rate is thermal energy developed, in W? What is the cost of operating the heater for a period of $4.0 \mathrm{~h}$ at $10 \phi / \mathrm{kW} \cdot \mathrm{h} ?$
$$
\begin{aligned}
W &=I^{2} R=(15 \mathrm{~A})^{2}(8.0 \Omega)=1800 \mathrm{~W}=1.8 \mathrm{~kW} \\
\text { Cost } &=(1.8 \mathrm{~kW})(4.0 \mathrm{~h})(10 \& / \mathrm{kW} \cdot \mathrm{h})=72 \epsilon
\end{aligned}
$$

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Key Concepts

Joule Heating

Joule heating is the phenomenon where an electric current flowing through a resistor generates heat. This process is governed by the principle that the thermal energy produced is proportional to the square of the current and the resistance, as expressed in the formula P = I²R.

Electrical Power Dissipation

Electrical power dissipation refers to the rate at which energy is converted into heat in a resistor. In the context of an electric heater, this concept is used to determine how quickly thermal energy is generated by the device, which is crucial for understanding its performance and impact on energy consumption.

Energy Consumption

Energy consumption is the total amount of energy used over a period of time. It is calculated by multiplying the power rating of an appliance by the duration of its operation, and is typically expressed in kilowatt-hours (kWh). This measure is important for assessing the overall energy usage of electrical devices.

Cost Calculation

Cost calculation in the context of electrical energy involves determining the monetary expense associated with energy consumption over time. Once the energy usage in kilowatt-hours is known, it is multiplied by the rate provided by the power company (cost per kWh) to find the total operating cost. This method is essential for budgeting and energy management.

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