You apply a potential difference of 4.50 V between the ends of a wire that is 2.50 m in length

step 1 You're given that a piece of wire has a potential difference of 4 .5 volts between its ends, and

You apply a potential difference of 4.50 V between the ends...

You apply a potential difference of $4.50 \mathrm{~V}$ between the ends of a wire that is $2.50 \mathrm{~m}$ in length and $0.654 \mathrm{~mm}$ in radius. The resulting current through the wire is $17.6 \mathrm{~A}$. What is the resistivity of the wire?

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Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates voltage (V), current (I), and resistance (R) through the equation V = IR. This relationship is key to analyzing and understanding how electrical circuits respond to applied voltages.

Resistivity

Resistivity is an intrinsic property of materials that quantifies how strongly a material opposes the flow of electric current. It is related to the resistance (R), length (L), and cross-sectional area (A) of a conductor through the formula R = ?L/A, providing a measure independent of the conductor's shape.

Cross-sectional Area Calculation

The cross-sectional area of a conductor, especially when it has a cylindrical shape, is calculated using the formula A = ?r², where r is the radius. This calculation is essential as it directly influences the resistance of the material and, ultimately, the resulting current.

Unit Conversion

Consistent unit usage is critical in physics calculations. Converting units, such as changing the wire's radius from millimeters to meters, ensures that all quantities in the equations are in the appropriate SI units, leading to accurate and meaningful results.

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