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Chapter 18: Problem 1

A battery charger delivers a current of \(3.0 \mathrm{A}\) for \(4.0 \mathrm{h}\) to a \(12-\mathrm{V}\) storage battery. What is the total charge that passes through the battery in that time?

Short Answer

Expert verified
Answer: 43200 C

Step by step solution

01

Convert time from hours to seconds

We are given the time in hours, but we need to convert it to seconds for the charge calculation. To do this, multiply by the number of minutes in an hour and the number of seconds in a minute: \(4.0 \mathrm{h} \times 60 \frac{\mathrm{min}}{\mathrm{h}} \times 60 \frac{\mathrm{s}}{\mathrm{min}} = 14400 \mathrm{s}\).
02

Use the formula to find the charge

Now we can use the formula for charge: \(Q = I \cdot t\). Plug in the values of current and converted time: \(Q = (3.0 \mathrm{A}) \times (14400 \mathrm{s})\).
03

Calculate the total charge

Perform the multiplication: \(Q = (3.0 \mathrm{A}) \times (14400 \mathrm{s}) = 43200 \mathrm{C}\). The total charge that passes through the battery in that time is \(43200 \mathrm{C}\).

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