Question

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?

Short answer

1. The charge is, $3.0\times {10}^{5}C$.
2. The potential energy is, $3.6\times {10}^{6}J$.

Step-by-step solution

Given

• The voltage of battery is, 12 V.
• The total charge of a battery is, 84 A.h.

Understanding the concept

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.

(a) Calculate the amount charge being represented

The amount of charge is expressed as,

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

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

(b) Calculate how much energy is involvedif the entire charge undergoes a change in electric potential of 12 V

The change in potential energy is expressed as,

$∆U=q∆V$

Substitute all the value in the above equation.

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

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