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Question 19.1: Suppose you have a 12.0 V motorcycle battery that can move 5...

Suppose you have a 12.0 V motorcycle battery that can move 5000 C of charge, and a 12.0 V car battery that can move 60,000 C of charge. How much energy does each deliver? (Assume that the numerical value of each charge is accurate to three significant figures.)
Strategy
To say we have a 12.0 V battery means that its terminals have a 12.0 V potential difference. When such a battery moves charge, it puts the charge through a potential difference of 12.0 V, and the charge is given a change in potential energy equal to ΔPE = qΔV .
So to find the energy output, we multiply the charge moved by the potential difference.

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For the motorcycle battery, q = 5000 C and ΔV = 12.0 V . The total energy delivered by the motorcycle battery is

\Delta PE _{\text {cycle }}=(5000 C )(12.0 V )                    (19.8)

= (5000 C)(12.0 J/C)

=6.00 \times 10^{4} J.

Similarly, for the car battery, q = 60,000 C and

\Delta PE _{ car }=(60,000 C )(12.0 V )                   (19.9)

=7.20 \times 10^{5} J.

Discussion

While voltage and energy are related, they are not the same thing. The voltages of the batteries are identical, but the energy supplied by each is quite different. Note also that as a battery is discharged, some of its energy is used internally and its terminal voltage drops, such as when headlights dim because of a low car battery. The energy supplied by the battery is still calculated as in this example, but not all of the energy is available for external use.

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