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Chapter 18: Problem 8

A Vespa scooter and a Toyota automobile might both use a \(12-\mathrm{V}\) battery, but the two batteries are of different sizes and can pump different amounts of charge. Suppose the scooter battery can pump 4.0 kC of charge and the automobile battery can pump \(30.0 \mathrm{kC}\) of charge. How much energy can each battery deliver, assuming the batteries are ideal?

Short Answer

Expert verified
Answer: The Vespa scooter battery can deliver 48,000 Joules of energy, while the Toyota automobile battery can deliver 360,000 Joules of energy.

Step by step solution

01

Write down the given information

The Vespa scooter battery has a voltage of 12 V and can pump 4.0 kC of charge. The Toyota automobile battery also has a voltage of 12 V and can pump 30.0 kC of charge.
02

Convert charge to Coulombs

First, we need to convert the given charge from kiloCoulombs (kC) to Coulombs (C): Vespa scooter battery charge: \(4.0\,\mathrm{kC} \times 1000 = 4000\,\mathrm{C}\) Toyota automobile battery charge: \(30.0\,\mathrm{kC} \times 1000 = 30000\,\mathrm{C}\)
03

Calculate energy for each battery

Now, we will use the formula Energy = Voltage 脳 Charge to determine the energy of each battery: Vespa scooter battery energy: \(E_{\text{Vespa}} = V_{\text{Vespa}} \times Q_{\text{Vespa}} = 12\,\mathrm{V} \times 4000\,\mathrm{C} = 48000\,\mathrm{J}\) Toyota automobile battery energy: \(E_{\text{Toyota}} = V_{\text{Toyota}} \times Q_{\text{Toyota}} = 12\,\mathrm{V} \times 30000\,\mathrm{C} = 360000\,\mathrm{J}\)
04

Present the final answers

The Vespa scooter battery can deliver 48000 Joules of energy, while the Toyota automobile battery can deliver 360000 Joules of energy.

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