Calculating Energy · Physics Playground

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 $ΔPE = q Δ V$ .

So to find the energy output, we multiply the charge moved by the potential difference.

Solution

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

\begin{array}{l} {ΔPE}_{cycle} & = & (5000 C) (12.0 V) \\ = & (5000 C) (12.0 J/C) \\ = & 6.00 \times 10^{4} J. \end{array}

19.8

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

\begin{array}{l} {ΔPE}_{car} & = & (60,000 C) (12.0 V) \\ = & 7.20 \times 10^{5} J. \end{array}

19.9

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.