Single Choice

When $$5V$$ potential difference is applied across a wire length $$0.1\ m$$, the drift speed of electron is 2.5 $$\times 10^{-4} ms^{-1}$$. If the electron density in the wire is 8 $$\times 10^{28} m^{-3}$$, the resistivity of the material is close to

A$$1.6\times 10^{-8}\ \Omega$$m
B$$1.6\times 10^{-7}\ \Omega$$m
C$$1.6\times 10^{-6}\ \Omega$$m
D$$1.6\times 10^{-5}\ \Omega$$m
Correct Answer

Solution

We know that
$$I=Ane{ v }_{ d }\\ \Rightarrow \dfrac { V }{ R } =Ane{ v }_{ d }\\ \Rightarrow \dfrac { V }{ \left( \rho \frac { l }{ A } \right) } =Ane{ v }_{ d }\\ \Rightarrow \dfrac { VA }{ \rho l } =Ane{ v }_{ d }\\ \Rightarrow \rho =\dfrac { V }{ lne{ v }_{ d } } =\dfrac { 5 }{ 0.1\times \left( 8\times { 10 }^{ 28 } \right) \times \left( 1.6\times { 10 }^{ -19 } \right) \times \left( 2.5\times { 10 }^{ -4 } \right) } =1.5625\times { 10 }^{ -5 }\ \Omega m\approx 1.6\times { 10 }^{ -5 }\ \Omega m$$

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