Chapter 24: Q1P (page 710)

A particular 12Vcar battery can send a total charge of 84 A.h(ampere-hours) through a circuit, from one terminal to the other. (a) How many coulombs of charge does this represent? (Hint:See Eq. 21-3.) (b) If this entire charge undergoes a change in electric potential of 12 V, how much energy is involved?

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Step by step solution

To calculate the total charge through the circuit, we note that 1A = 1C/s and 1h = 3600s.

Potential difference is the change of potential energy per unit charge.

Using the equation of potential energy U = qV, we can find change in potential energy.

The amount of charge is expressed as,

$\begin{array}{rcl} 84 A . h & = & [84 \frac{C . h}{s}] [3600 \frac{s}{h}] \\ = & 3.0 \times 10^{5} C \end{array}$

Hence the charge is, $\begin{array}{rcl} 3.0 \times 10^{5} C \end{array}$ .

The change in potential energy is expressed as,

$∆ U = q ∆ V$

Substitute all the value in the above equation.

$\begin{array}{rcl} ∆ U & = & (3.0 \times 10^{5} C) (12 V) \\ = & 3.6 \times 10^{6} J \end{array}$

Hence the potential energy is, $3.6 \times 10^{6} J$ .

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