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Chapter 27: Q. 48 (page 764)

A 1.5m long wire is made of a metal with the same electron density as copper. The wire is connected across the terminals of a 9.0V battery. What conductivity would the metal need for the drift velocity of electrons in the wire to be 60mph? By what factor is this larger than the conductivity of copper?

Short Answer

Expert verified

The factor the given metal is larger than the conductivity of copper is6.07×1010,1000times.

Step by step solution

01

Given Information 

The given metal wire length=1.5m

Voltage=9.0V

Drift velocity=60mph

02

Explanation 

Find the conductance as

J=σE⇒σ=JE

Density of electrons, elementary charge, and drift speed are used in calculating current density,,

J=enevd

The electric field inside a wire of length Lunder potential difference Uis,

E=UL

We find that by substituting these two expressions at the conductance expression, we get

σ=enevdLUJ

Here, 60mph=26.8m/s

Substitute the values,

role="math" localid="1649139392068" σ=1.6×10-19C×8.5×1028e×26.8m/s×1.5m9V

σ=6.07×1010S.

03

Final Answer

This value is 1000 times greater than the value of copper,σCu=6×107s.

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