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

How much does it cost to run for one day? Round to the nearest cent. $Answer

Answer 1

Approximately
`\$ 3.02`.

Step-by-step 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 * 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} * \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} * \text{current} \\ &= 240\; {\rm V} * 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} * \text{time} \\ &= 5.04\; {\rm kW} * 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.)