P 2.4-8 The portable lighting equipment for a mine is located 100 meters from its dc supply source. The mine lights use a total of 5 kW and operate at 120 V dc. Determine the required cross-sectional area of the copper wires used to connect the source to the mine lights if we require that the power lost in the copper wires be less than or equal to 5 percent of the power required by the mine lights.

Hint: Model both the lighting equipment and the wire as resistors.

Here is the basic circuit we are dealing with

Resistance of cross-sectional area contributes to resistance by the relationship

We know L = 100. m and we can look up that

Area will be found from

Power lost in the wires is said to be 5% of total power

The 2 is due to the need for two wires to complete the circuit.

Power lost in a wire is joule heating

Power used by lights come from

Since the circuit is a series circuit,

Solving for Resistance of the wire

Now we can find the area

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This page last updated on December 27, 2018