   Chapter 17, Problem 63AP

Chapter
Section
Textbook Problem

A length of metal wire has a radius of 5.00 × 10−3 m and a resistance of 0.100 Ω. When the potential difference across the wire is 15.0 V, the electron drift speed is found to be 3.17 × 10−4 m/s. On the basis of these data, calculate the density of free electrons in the wire.

To determine
The free electron density in the metal wire.

Explanation

Given Info: The metal wire has radius 5.00×103m and the resistance is 0.100Ω . The potential difference applied across the wire is 15.0V . The drift speed of electron is 3.17×104ms1 .

Explanation:

Formula to calculate the current is,

I=ΔVR

• I is the current in the wire,
• ΔV is the potential difference across the wire,
• R is the resistance of the wire,

Formula to calculate the free electron density is,

n=IeAvd

• n is the free electron density,
• e is the charge of electron,
• A is the area of cross section of wire,
• vd is the drift velocity of electron,

Formula to calculate the area is,

A=πr2

• r is the radius of wire,

Use πr2 for A and ΔV/R for I in the n=I/eAvd to rewrite it.

n=ΔV/Re(πr2)vd=ΔVeR(πr2)vd

Substitute 15.0V for ΔV , 0

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