A 14 gauge copper wire of diameter 1.628 mm carries a current of 12.5 mA. (a) What is the poten

step 1 Alright, so in this problem, in part A, so we have a copper as the material of the wire, and the

A 14 gauge copper wire of diameter 1.628 mm carries a...

A 14 gauge copper wire of diameter $1.628 \mathrm{~mm}$ carries a current of 12.5 mA. (a) What is the potential difference across a $2.00 \mathrm{~m}$ length of the wire? (b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else were the same?

Key Concepts

Cross-sectional Area Calculation

The cross-sectional area of a conductor, often required when calculating its resistance, is especially important for wires, which are typically cylindrical. The area (A) is computed using the formula A = ?r², where r is the radius of the wire. This calculation is essential to understanding how size and geometry impact the resistance of the conductor.

Resistance Calculation in Conductors

The resistance of a conductor can be calculated using the formula R = ?L/A, where ? is the material's resistivity, L is the length of the conductor, and A is its cross-sectional area. This concept ties together the effects of the conductor's material properties and its physical dimensions, and it is key to determining the voltage drop across the conductor using Ohm's Law.

Ohm's Law

Ohm's Law is a fundamental principle in electricity that establishes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit (V = IR). It allows calculation of one variable when the other two are known, and it is essential for analyzing circuits involving different materials and geometries.

Resistivity of Materials

Resistivity is an intrinsic property of materials that quantifies how strongly a given material opposes the flow of electric current. Different materials have different resistivities; for example, silver has a lower resistivity than copper, meaning it allows current to pass more easily. This concept is crucial for determining how material choice affects the overall resistance and potential difference in conductors.

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