An electric utility company supplies a customer's house from...

An electric utility company supplies a customer's house from the main power lines $(120 \mathrm{V})$ with two copper wires, each of which is $50.0 \mathrm{m}$ long and has a resistance of $0.108 \Omega$ per $300 \mathrm{m} .$ (a) Find the voltage at the customer's house for a load current of 110 A. For this load current, find (b) the power the customer is receiving and (c) the electric power lost in the copper wires.

Key Concepts

Conductor Resistance and Series Circuit Analysis

The resistance of a conductor is determined by the material properties, its length, and cross-sectional area. In a series circuit, the individual resistances add up, meaning that for power transmission through two wires, the total resistance is the sum of the resistances of each wire. This total resistance is then used to compute the overall voltage drop and subsequent power losses in the circuit.

Electrical Power Calculations

Electrical power can be calculated in multiple ways, including as the product of voltage and current (P = I × V) for the load, and as the power lost due to resistance in the conductors using the formula P = I² × R. These calculations are essential for evaluating both the useful power that the customer receives and the power dissipated as heat in the wiring.

Ohm's Law

This is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = I × R. It is instrumental in determining how much voltage is dropped across a component when current flows through it, and it forms the basis for analyzing how electrical systems operate.

Voltage Drop in Transmission Lines

When current flows through conductors such as copper wires, which have inherent resistance, a portion of the supplied voltage is lost as a drop along the length of the wire. Calculating the voltage drop is essential in ensuring that adequate voltage reaches the load, and it typically utilizes Ohm's law to determine the loss based on the resistance of the conductors and the amount of current flowing through them.

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