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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 cents/kWh?9.00\ \mathrm{cents/kW} \cdot \mathrm{h} ?

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1 Concepts and Principles

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

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

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

P=I2R=(ΔV)2R\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- Power\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 Δt\Delta t in which the process occurred:

P=ΔEΔt\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  W=1  J/s1\;\mathrm{W}=1\;\mathrm{J/s}).

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