A cylindrical copper cable 1.50 km long is connected across...

Name: Problem 68, Chapter 25: University Physics with Modern Physics
Uploaded: 2019-04-05T05:42:12-08:00
Duration: 4 min 48 s
Channel: Ryan Kutayiah
Description: A cylindrical copper cable 1.50 km long is connected across a 220.0-V potential difference. (a) What should be its diameter so that it produces heat at a rate of 90.0 W? (b) What is the electric field inside the cable under these conditions?

A cylindrical copper cable 1.50 km long is connected across a 220.0-V potential difference. (a) What should be its diameter so that it produces heat at a rate of 90.0 W? (b) What is the electric field inside the cable under these conditions?

Key Concepts

Resistivity of Materials

Resistivity is a fundamental property that quantifies how strongly a material opposes the flow of electric current. It is used to calculate the resistance of a conductor when combined with its length and cross?sectional area. In problems like this, knowing the resistivity of copper is essential to determine the appropriate conductor dimensions for a specified electrical performance.

Conductor Geometry (Cylindrical Conductors)

The geometry of a cylindrical conductor, particularly its cross-sectional area and length, directly affects its electrical resistance. The resistance is inversely proportional to the area and directly proportional to the length, with the area calculated from the diameter. Understanding this relationship is crucial when designing cables to meet specific resistance, power, or heating requirements.

Ohm's Law

Ohm’s Law is a foundational principle in electrical circuits that states the relationship between voltage, current, and resistance (V = IR). It forms the basis for analyzing how a potential difference applied across a conductor results in a current, and it is instrumental in relating these quantities to the conductor’s physical properties.

Power Dissipation in Resistors

The rate at which electrical energy is converted to heat in a resistor is governed by the power dissipation formulas, such as P = V^2/R. This concept is critical in applications where controlling heat generation is necessary, as it links the electrical parameters (voltage and resistance) to the thermal output of the conductor.

Electric Field in a Conductor

The electric field within a uniformly conducting material can be determined by the gradient of the electric potential, given by E = V/L. This concept helps in understanding how the voltage applied over a given length of material establishes an electric field, which in turn drives the current through the conductor.

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