Chapter 26, Problem 72A

To determine

To Find: The daily electric power cost of operating an air compressor.

Answer to Problem 72A

The daily cost of the air condition is $\text{\$1}\text{.653}\text{per}\text{day}$ .

Explanation of Solution

Given:

The current flow through the air compressor is $I=12\text{A}$ .

Voltage of the air compressor is $V=245\text{V}$ .

Cost per $\text{KWh}$ is $\text{\$}\text{0}\text{.095}\text{KWh}$ .

Formula:

The power deliver by the a source is

  $P=IV$   ...... (1)

Calculation:

Substitute $12\text{A}$ for $\text{I}$ and $245\text{V}$ for $V$ in equation (1)

  $\begin{array}{c}P=IV\\ =12\times 245\\ =2940\text{W}\\ \text{=2}\text{.9}\text{KW}\end{array}$

Power of the air condition is $\text{2}\text{.9 KW}$ .

Now, cost of the air condition power per hour is

  $\begin{array}{l}\text{=\$}\text{0}\text{.095}\text{KWh}\times \text{2}\text{.9 KW}\\ =\$0.2755\text{/h}\end{array}$

Given that the air condition is runs $\frac{1}{4}$ th of day i.e.

  $\begin{array}{l}=\frac{1}{4}\times 24\text{hour}\\ =6\text{hour}\end{array}$

Therefore the power cost of the air condition per day is

  $\begin{array}{l}=\$0.2755\times 6\text{hour}\\ \text{=\$1}\text{.653}\text{per}\text{day}\end{array}$

Conclusion:

Hence, the required daily cost of the air condition is $\text{\$1}\text{.653}\text{per}\text{day}$ .