A copper wire has radius r=0.0250 cm, is 3.00 m long, has resistivity ρ=1.72 ·10^-5 Ωm, and ca

step 1 This question, we have copper wire of radius small r equals to 0 .0250 centimeter, that is, 0 .0

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 $\rho=1.72 \cdot 10^{-5} \Omega \mathrm{m},$ and carries a current of $0.400 \mathrm{~A}$. The wire has a charge-carrier density of $8.50 \cdot 10^{24}$ electrons/m $^{3}$ a) What is the resistance, $R,$ of the wire? b) What is the clectric potential difference, $\Delta V$, across the wire? c) What is the electric field. F. in the wire?

A copper wire has radius $r=0.0250 \mathrm{~cm},$ is $3.00 \mathrm{~m}$ long, has resistivity $\rho=1.72 \cdot 10^{-5} \Omega \mathrm{m},$ and carries a current of $0.400 \mathrm{~A}$. The wire has a charge-carrier density of $8.50 \cdot 10^{24}$ electrons/m $^{3}$
a) What is the resistance, $R,$ of the wire?
b) What is the clectric potential difference, $\Delta V$, across the wire?
c) What is the electric field. F. in the wire?

Key Concepts

Electric Field in a Conductor

The electric field within a conductor can be determined by the potential difference (voltage) across it and its length. The relationship is given by E = ?V/L, where E is the electric field, ?V is the voltage difference, and L is the length over which the voltage is applied. This concept is important in understanding how an electric field drives the flow of charges through a conductor.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates the voltage across a conductor to the current flowing through it and its resistance. The law is typically expressed as V = IR, where V is the voltage, I is the current, and R is the resistance. It provides a direct connection between these key electrical quantities.

Electrical Resistivity

Electrical resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is usually denoted by the Greek letter ? and is measured in ohm-meters. A lower resistivity means the material is a better conductor, while a higher resistivity implies that the material is more resistant to current flow.

Resistance Calculation

The resistance of a conductor depends on both its material properties and its geometry. It is given by the formula R = ?L/A, where ? is the resistivity, L is the length of the conductor, and A is the cross-sectional area. This relationship shows that a longer conductor or one with a smaller cross-sectional area has a higher resistance.

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