Batteries are rated in terms of ampere-hours (A ·h) : For...

Batteries are rated in terms of ampere-hours $(\mathrm{A} \cdot \mathrm{h})$ : For example, a battery that can produce a current of $2.00 \mathrm{~A}$ for $3.00 \mathrm{~h}$ is rated at $6.00 \mathrm{~A} \cdot \mathrm{h} .(\mathrm{a})$ What is the total energy, in kilowatt-hours, stored in a $12.0$ -V battery rated at $55.0 \mathrm{~A} \cdot \mathrm{h} ?$ (b) At a rate of $\$ 0.0600$ per kilowatt-hour, what is the value of the electricity produced by this battery?

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Key Concepts

Energy Cost Calculation

Determining the cost of stored or consumed energy involves multiplying the total energy by the price per energy unit. In this context, once the energy in kilowatt-hours is determined, it can be directly multiplied by the cost rate to find the monetary value of the energy available or used.

Unit Conversions (Watt-hours to Kilowatt-hours)

Watt-hours and kilowatt-hours are units used for measuring electrical energy. Since 1 kilowatt-hour is equal to 1000 watt-hours, converting between these units is necessary when dealing with energy calculations and cost evaluations, ensuring consistency with billing or energy consumption measurements.

Ampere-Hour Rating

Ampere-hour is a unit of electric charge used to describe the capacity of a battery. It represents the amount of current a battery can supply over the course of one hour. This metric allows us to quantify how long a battery can operate before its stored charge is exhausted.

Voltage and Energy Relationship

Voltage is the electrical potential difference that drives current through a circuit, and when it is multiplied by charge (or current over time), it yields the energy stored or delivered by the battery. In batteries, the product of voltage and ampere-hour rating gives the total energy in watt-hours.

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