Question

An air conditioner runs 15 minutes each hour on a hot summer day. It is on a 240 volt circuit and uses 21 amps. Rate is $.10/kWh

Answer 1

Answer:

Approximately $\ 3.02$.

Explanation:

Note that the electric rate in this question is in the unit dollar-per-${\rm kWh}$, where $1\; {\rm kWh}$ is the energy to run an appliance of power $1\; {\rm kW}$ for an hour.

Number of minutes for which the air conditioner is running in that day: $15 \times 24 = 360\; \text{minute}$. Apply unit conversion and ensure that this time is measured in hours (same as the unit of the electric rate.)

$\begin{aligned} \text{time} &= 360\; \text{minute} \times \frac{1\; \text{hour}}{60\; \text{minute}} = 6\; \text{hour} \end{aligned}$.

The power of this air conditioner is:

$\begin{aligned} \text{power} &= \text{voltage} \times \text{current} \\ &= 240\; {\rm V} \times 21\; {\rm A} \\ &= 5040\; {\rm W} \\ &= 5.04\; {\rm kW} \end{aligned}$.

Thus, the energy that this air conditioner would consume would be:

$\begin{aligned}\text{energy} &= \text{power} \times \text{time} \\ &= 5.04\; {\rm kW} \times 6\; \text{hour} \\ &= 30.24\; {\rm kWh} \end{aligned}$.

At a rate of $0.1$ dollar-per-${\rm kWh}$, the cost of that much energy would be approximately $3.02$ dollars (rounded to the nearest cent.)