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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 × 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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Most popular questions from this chapter

About \(5.0 \times 10^{4} \mathrm{m}\) above Earth's surface, the atmosphere is sufficiently ionized that it behaves as a conductor. The Earth and the ionosphere form a giant spherical capacitor, with the lower atmosphere acting as a leaky dielectric. (a) Find the capacitance \(C\) of the Earth-ionosphere system by treating it as a parallel plate capacitor. Why is it OK to do that? [Hint: Com- pare Earth's radius to the distance between the "plates." (b) The fair-weather electric field is about \(150 \mathrm{V} / \mathrm{m},\) downward. How much energy is stored in this capacitor? (c) Due to radioactivity and cosmic rays, some air molecules are ionized even in fair weather. The resistivity of air is roughly \(3.0 \times 10^{14} \Omega \cdot \mathrm{m}\) Find the resistance of the lower atmosphere and the total current that flows between Earth's surface and the ionosphere. [Hint: since we treat the system as a parallel plate capacitor, treat the atmosphere as a dielectric of uniform thickness between the plates.] (d) If there were no lightning, the capacitor would discharge. In this model, how much time would elapse before Earth's charge were reduced to \(1 \%\) of its normal value? (Thunderstorms are the sources of emf that maintain the charge on this leaky capacitor.)
A battery has a terminal voltage of \(12.0 \mathrm{V}\) when no current flows. Its internal resistance is \(2.0 \Omega .\) If a \(1.0-\Omega\) resistor is connected across the battery terminals, what is the terminal voltage and what is the current through the \(1.0-\Omega\) resistor?
A battery has a \(6.00-\mathrm{V}\) emf and an internal resistance of $0.600 \Omega$. (a) What is the voltage across its terminals when the current drawn from the battery is \(1.20 \mathrm{A} ?\) (b) What is the power supplied by the battery?
A person can be killed if a current as small as \(50 \mathrm{mA}\) passes near the heart. An electrician is working on a humid day with hands damp from perspiration. Suppose his resistance from one hand to the other is $1 \mathrm{k} \Omega$ and he is touching two wires, one with each hand. (a) What potential difference between the two wires would cause a 50 -mA current from one hand to the other? (b) An electrician working on a "live" circuit keeps one hand behind his or her back. Why?
(a) In a charging \(R C\) circuit, how many time constants have elapsed when the capacitor has \(99.0 \%\) of its final charge? (b) How many time constants have elapsed when the capacitor has \(99.90 \%\) of its final charge? (c) How many time constants have elapsed when the current has \(1.0 \%\) of its initial value?
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