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Question

# A small office-building air conditioner operates on 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (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 $9.00\ \mathrm{cents/kW} \cdot \mathrm{h} ?$

Solution

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### 1 Concepts and Principles

1- If a potential difference $\Delta V$ is maintained across a circuit element, the $\textbf{power}$, or rate at which energy is supplied to the element, is

$\begin{gather*} P=I\Delta V \end{gather*}$

Because the potential difference across a resistor is given by $\Delta V=IR$, we can express the power delivered to a resistor as

$\begin{gather*} P = I^2 R = \dfrac{(\Delta V)^2}{R} \tag{1} \end{gather*}$

The energy delivered to a resistor be electrical transmission appears in the form of internal energy in the resistor.

2- $\textbf{Power}$: The power of a process is the amount of some type of energy converted into a different type divided by the time interval $\Delta t$ in which the process occurred:

$\begin{gather*} P=\dfrac{\Delta E}{\Delta t} \tag{2} \end{gather*}$

The SI unit of power is the watt (W). 1 watt is 1 joule/second ($1\;\mathrm{W}=1\;\mathrm{J/s}$).

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