A car battery is rated at 90 A h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the battery?

검증된 단계별 안내

Understand the relationship between current, time, and charge. The total charge (Q) that flows through a circuit is given by the formula:

Q = I t

, where

Q

is the charge in coulombs,

I

is the current in amperes, and

t

is the time in seconds.

Convert the time from hours to seconds. Since there are 3600 seconds in an hour, multiply the given time (1 hour) by 3600 to express it in seconds:

t = 1 h (3600 s / h)

Substitute the given values into the formula. The current

I

is 90 A, and the time

t

is the value you calculated in seconds. The formula becomes:

Q = 90 (3600)

Perform the multiplication to find the total charge in coulombs. Remember that 1 ampere-second is equal to 1 coulomb, so the result will be in coulombs.

Interpret the result. The total charge leaving the battery is the product of the current and the time, expressed in coulombs. This value represents the total amount of electric charge that the battery can supply before being completely discharged.

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주요 개념

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Ampere-Hour (A h)

An Ampere-Hour (A h) is a unit of electric charge that represents the amount of charge transferred by a steady current of one ampere flowing for one hour. In the context of a car battery rated at 90 A h, it indicates that the battery can deliver 90 amperes of current for one hour before depletion, which is crucial for understanding battery capacity.

Charge (Q)

Electric charge, denoted as Q, is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It is measured in coulombs (C), and the total charge that leaves the battery can be calculated by multiplying the current (in amperes) by the time (in hours) the current flows, providing a direct link to the battery's capacity.

Current (I)

Current (I) is the flow of electric charge in a circuit, measured in amperes (A). It represents the rate at which charge is flowing, and in this scenario, knowing the current drawn by the headlights allows us to determine how long the battery can sustain that current before it is fully discharged, thus linking current to the total charge delivered.