The label on a 12.0 V truck battery states that it is rated at 180.0 A ·h (ampere-hours). Treat

step 1 so in this volume we are given the voltage is equal to 12 volts and current rate is equal to 180

The label on a 12.0 V truck battery states that it is rated...

The label on a $12.0 \mathrm{V}$ truck battery states that it is rated at $180.0 \mathrm{A} \cdot \mathrm{h}$ (ampere-hours). Treat the battery as ideal. (a) How much charge in coulombs can be pumped by the battery? [Hint: Convert A.h to A.s.] (b) How much electric energy can the battery supply? (c) Suppose the radio in the truck is left on when the engine is not running. The radio draws a current of 3.30 A. How long does it take to drain the battery if it starts out fully charged?

The label on a $12.0 \mathrm{V}$ truck battery states that it is rated at $180.0 \mathrm{A} \cdot \mathrm{h}$ (ampere-hours). Treat the battery as ideal.
(a) How much charge in coulombs can be pumped by the battery? [Hint: Convert A.h to A.s.] (b) How much electric energy can the battery supply?
(c) Suppose the radio in the truck is left on when the engine is not running. The radio draws a current of 3.30 A. How long does it take to drain the battery if it starts out fully charged?

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Key Concepts

Ampere-Hour to Coulomb Conversion

Ampere-hours is a unit that quantifies electric charge by combining current (in amperes) with time (in hours). Since one hour is 3600 seconds, converting ampere-hours to coulombs involves multiplying by 3600, allowing a precise calculation of the total charge that a battery can supply.

Electric Energy in a Battery

The electric energy stored in a battery can be determined by multiplying the charge (in coulombs) by the voltage (in volts). This relationship, expressed as energy (in joules) equals charge times voltage, is fundamental in understanding how a battery's stored charge is converted into usable energy.

Current, Charge, and Time Relationship

The equation Q = I × t connects current, charge, and time, where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds. This relationship is essential when calculating how long a battery will last under a continuous load, such as determining the time required to drain the battery at a known current draw.

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