Batteries are rated in terms of ampere-hours (A ·h ) . For example, a battery that can deliver a

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

Batteries are rated in terms of ampere-hours (A $\cdot \mathrm{h} )$ . For example, a battery that can deliver a current of 3.0 $\mathrm{A}$ for 5.0 $\mathrm{h}$ is rated at 15 $\mathrm{A} \cdot \mathrm{h}$ . (a) What is the total energy, in kilowatt-hours, stored in a $12-\mathrm{V}$ battery rated at 55 $\mathrm{A} \cdot \mathrm{h}$ ? (b) At $\$ 0.12$ per kilowatt hour, what is the value of the electricity that can be produced by this battery?

Key Concepts

Ampere-hour Rating

Ampere-hour (A·h) is a unit of electric charge commonly used to rate battery capacity. It represents the amount of current a battery can provide over a specific period, typically one hour. For example, a battery rated at 55 A·h can, in theory, deliver 55 amperes for one hour or a lower current for a proportionately longer time. This rating is essential to determine the energy storage capability of the battery when combined with its voltage.

Energy Stored in a Battery

The energy stored in a battery can be calculated by multiplying its voltage (in volts) by its ampere-hour rating, which gives the energy in watt-hours. This relationship illustrates how the capacity (in A·h) and the voltage determine the total energy that can be delivered by the battery. Converting this value into kilowatt-hours (kWh) makes it easier to compare with typical electrical energy consumption and pricing.

Unit Conversions (Watt-hours to Kilowatt-hours)

Unit conversion is a critical step in energy calculations. Since 1 kilowatt-hour is equivalent to 1,000 watt-hours, converting the energy expressed in watt-hours to kilowatt-hours involves dividing by 1,000. This conversion is necessary when evaluating practical energy storage systems or comparing energy amounts to electric bills, which are commonly measured in kWh.

Electricity Pricing

Electricity pricing involves determining the monetary value of the energy stored or consumed, typically expressed in dollars per kilowatt-hour. By calculating the energy in kWh and multiplying by the cost per kilowatt-hour, one can find the economic value of the battery’s stored energy. This concept is important for understanding cost efficiency and economic assessments in energy storage and consumption scenarios.

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