Chapter 22, Problem 76A

To determine

The cost per $\text{kWh}$ of the battery.

Answer to Problem 76A

  $\$512.82\text{per kWh}$

Explanation of Solution

Given:

The current deliver by a battery, $I=0.0250\text{A}$

The voltage supplied by a battery, $V=9.0\text{V}$

The time, $t=26.0\text{h}$

The cost of the battery, $C=\$3.00$

Formula used:

The electric power $\left(P\right)$ across a circuit is given by,

  $P=IV$

Where, I is the current and V is the potential difference.

And, the energy $\left(E\right)$ during time $t$ is given by,

  $\begin{array}{c}E=Pt\\ =VIt\end{array}$

Calculation:

Energy that will be delivered by the battery during $t=26.0\text{h}$ will be,

  $\begin{array}{c}E=VIt\\ =\left(9.0\right)\left(0.025\right)\left(26\right)\\ =5.85\text{Wh}\\ =0.00585\text{kWh}\end{array}$

Then, cost per $\text{kWh}$ of the battery will be,

  $\begin{array}{c}C\text{'}=\frac{C}{E}\\ =\frac{\$3.0}{0.00585\text{kWh}}\\ =\$512.82\text{per kWh}\end{array}$

Conclusion:

Hence, thecost per $\text{kWh}$ of the battery is $\$512.82\text{per kWh}$ .