Question

A small office building air conditioner operates on 412 V AC and consumes 49.5 kW.(a) What is its effective resistance (in Ω)? Ω(b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs 9.00 cents/kW·h?$

Answer 1

(a)

In order to calculate the resistance of the air conditioner, we can use the formula below:

`P=(V^2)/(R)`

Where P is the power (in W), V is the voltage (in V) and R is the resistance (in ohms).

So, for P = 49500 W and V = 412 V, we have:

`\begin{gathered} 49500=(412^2)/(R)\\ \\ R=(412^2)/(49500)\\ \\ R=3.429\text{ ohms} \end{gathered}`

(b)

If the air conditioner is used 8 hours per day for 30 days, the total number of hours is 240 h.

Multiplying the power (in kW) by the time (in h), we have the energy (in kWh):

`\begin{gathered} E=P\cdot t\\ \\ E=49.5\cdot240\\ \\ E=11880\text{ kWh} \end{gathered}`

each kWh of energy costs 9 cents, so the total cost is:

`\begin{gathered} Cost=11880\cdot0.09\\ \\ Cost=\$1069.20 \end{gathered}`

Therefore the cost is $1069.20.