A copper wire has radius r=0.0250 cm, is 3.00 m long, has resistivity ρ=1.72 ·10^-8 Ωm, and ca

step 1 with a given problem radius of upper wire is given as r is equal to 0 .0 250 centimeter which ca

A copper wire has radius r=0.0250 cm, is 3.00 m long, has...

A copper wire has radius $r=0.0250 \mathrm{~cm},$ is $3.00 \mathrm{~m}$ long, has resistivity $\rho=1.72 \cdot 10^{-8} \Omega \mathrm{m},$ and carries a current of $0.400 \mathrm{~A}$. The wire has density of charge carriers of $8.50 \cdot 10^{28}$ electrons $/ \mathrm{m}^{3}$ a) What is the resistance, $R,$ of the wire? b) What is the electric potential difference, $\Delta V$, across the wire? c) What is the electric field, $E$, in the wire?

A copper wire has radius $r=0.0250 \mathrm{~cm},$ is $3.00 \mathrm{~m}$ long, has resistivity $\rho=1.72 \cdot 10^{-8} \Omega \mathrm{m},$ and carries a current of $0.400 \mathrm{~A}$. The wire has density of charge carriers of $8.50 \cdot 10^{28}$ electrons $/ \mathrm{m}^{3}$
a) What is the resistance, $R,$ of the wire?
b) What is the electric potential difference, $\Delta V$, across the wire?
c) What is the electric field, $E$, in the wire?

Key Concepts

Resistance Calculation

This concept involves determining the resistance of a conductor by using its physical dimensions and intrinsic material property called resistivity. The resistance is calculated using the formula R = ?L/A, where ? is the resistivity, L is the length of the conductor, and A is its cross-sectional area. This relationship shows how geometry and material composition influence the opposition to current flow.

Ohm's Law

Ohm's Law is a fundamental principle in electricity which states that the voltage across a conductor is directly proportional to the current flowing through it, with the proportionality constant being the resistance (V = IR). This law is crucial for analyzing circuits and understanding how voltage, current, and resistance interrelate in any electrical conductor.

Electric Field in a Conductor

The electric field within a conductor is defined as the force per unit charge experienced by a charge in the material. It can be determined by dividing the electric potential difference by the length over which that drop occurs (E = ?V/L). This concept is important because it connects the macroscopic measurement of voltage with the microscopic forces that drive the motion of charge carriers.

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