Ch 27: Current and Resistance

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 27: Current and Resistance

Problem 53c

Chapter 27, Problem 53c

Electrical engineers sometimes use a wire's conductance, G=σA/L, instead of its resistance. A 1.5 A current flows through the wire of part b. What is the potential difference between the ends of the wire?

Verified step by step guidance

Start by understanding the relationship between conductance (G), resistance (R), and Ohm's Law. Conductance is the reciprocal of resistance: G = 1/R. Ohm's Law states that V = IR, where V is the potential difference, I is the current, and R is the resistance.

From the given formula for conductance, G = σA/L, where σ is the conductivity of the material, A is the cross-sectional area of the wire, and L is the length of the wire, calculate the conductance if σ, A, and L are known.

Once the conductance (G) is determined, calculate the resistance (R) using the relationship R = 1/G.

Using the resistance (R) and the given current (I = 1.5 A), apply Ohm's Law (V = IR) to calculate the potential difference (V) across the wire.

Substitute the values of I and R into the equation V = IR to find the potential difference. Ensure all units are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conductance

Conductance (G) is a measure of how easily electricity flows through a material. It is the reciprocal of resistance (R), defined as G = 1/R. In the formula G = σA/L, σ represents the material's conductivity, A is the cross-sectional area of the wire, and L is its length. Higher conductance indicates a better ability to conduct electric current.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = IR. This law is fundamental in electrical engineering for analyzing circuits and understanding the relationship between voltage, current, and resistance.

Potential Difference

Potential difference, also known as voltage, is the difference in electric potential energy per unit charge between two points in an electric field. It is what drives the flow of electric current in a circuit. In the context of the given question, the potential difference can be calculated using Ohm's Law, where V = IR, allowing us to find the voltage across the wire when the current and resistance are known.

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