Chapter 22, Problem 80A

To determine

The amount of current that the air conditioner will take from a $120\text{V}$ outlet.

Answer to Problem 80A

  $12.86\text{A}$

Explanation of Solution

Given:

The cost of operation of air conditioner, $C_t=\$50\text{per 30 days}$

The number of days, air conditioner is expected to run, $t=15\text{days}$

The electricity cost per kWh, $C\text{'}=\$0.090\text{per kWh}$

The potential, $\Delta V=120\text{V}$

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.

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

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

Calculation:

Using the given values, the total energy consumption of air conditioner will be,

  $\begin{array}{c}E=\frac{C_t}{C\text{'}}\\ =\frac{50}{0.090}\\ =555.56\text{kWh}\end{array}$

Then, using the formula of energy consumption, the amount of current that air conditioner will draw from a $120\text{V}$ outlet is,

  $\begin{array}{c}E=VIt\\ 555.56\text{kWh}=\left(120\right)\left(I\right)\left(15\text{days}\right)\\ 555.56\times {10}^3=\left(120\right)\left(I\right)\left(15\text{days}\times \frac{24\text{h}}{1\text{day}}\right)\\ I=12.86\text{A}\end{array}$

Conclusion:

Hence, the amount of current drawn by the air conditioner is $12.86\text{A}$ .