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Chapter 25: Problem 13

What would happen to the drift velocity of electrons in a wire if the resistance due to collisions between the electrons and the atoms in the crystal lattice of the metal disappeared?

Short Answer

Expert verified
Answer: When the resistance due to collisions between electrons and atoms in the crystal lattice is removed, the drift velocity of the electrons in the wire would increase as a result of fewer collisions and more efficient movement of electrons through the wire.

Step by step solution

01

Understand the drift velocity of electrons in a wire

Drift velocity is the average velocity of electrons in a conductive material like a wire, due to an applied electric field. This drift velocity is quite slow as the electrons are constantly colliding with the atoms in the metal, which cause resistance.
02

Relationship between drift velocity and resistance

The drift velocity (v_d) of electrons in a wire can be calculated using the formula: v_d = I / (n * e * A) where I is the current through the wire, n is the number of electrons per unit volume, e is the charge of an electron, and A is the cross-sectional area of the wire. The resistance (R) of the wire is calculated using Ohm's law: R = V / I where V is the voltage across the wire and I is the current through the wire. In a metal, the resistance is mainly due to collisions between the electrons and the atoms in the lattice. These collisions slow down the electrons and decrease their overall drift velocity.
03

Effect of removing resistance due to collisions

If the resistance due to collisions between electrons and atoms in the crystal lattice were to disappear, the electrons would no longer be slowed down in their path. This means that they would experience fewer collisions and would be able to move more freely through the metal. As a result, the drift velocity of electrons in the wire would increase. In other words, without the resistance due to collisions, the electrons would move more efficiently through the wire, causing a decrease in the time it takes for them to travel through the conductive material. Consequently, the drift velocity of the electrons would increase.
04

Conclusion

In conclusion, if the resistance due to collisions between electrons and atoms in the crystal lattice of a metal were to disappear, the drift velocity of the electrons would increase as a result of fewer collisions and more efficient movement of electrons through the wire.

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