Chapter 26

# Chapter 26 - Current, Resistivity, Resistance In our...

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Current, Resistivity, Resistance In our discussion of capacitors we talked of charging and discharging them, which means moving charge onto and off of the capacitor plates, respectively. This happens by the flow of charge through the electrical conductors . We now consider this flow of charge in greater detail. We begin with a piece of wire not yet connected to a power supply. At room temperature the atoms making up the lattice of any material possess thermal energy, oscillating about their equilibrium positions. Microscopic segment of wire

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oscillating + atom ( low temperature ) In a highly conducting metal like silver, the atoms each give up one of its electrons to let them wander freely throughout the body of the wire. This leaves the oscillating atomic cores positively charged . electron trajectory wire If these positively charged core atoms are nearly at rest (like happens if we cool the wire to near absolute zero ) an electron in motion experiences the atoms as a homogeneous background of positive charge through which it can move, nearly unperturbed. Electrons that reach the boundaries of the wire are reflected back by their attraction to the positive atomic cores.
At higher temperatures , where the vibration amplitudes are greater the accumulation of – charge where two core atoms happen to diverge from each other presents a barrier from which the electrons are scattered . electron trajectory oscillating atom The resulting trajectory of a single electron is represented below. The lattice vibrations themselves propagate as waves called phonons so we say that the electrons are scattered by the phonons . The electron speeds are ~ 10 6 m/s but they are frequently redirected by these scattering events. In copper, at room temperature, the mean free time between such scattering collisions for an electron is ~10 –14 s and the mean free path (distance traveled between scattering events is ~40 nm (sample problem 26–6) (~ every 5 th core atom represented)

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electron trajectory oscillating atom wire Because there are as many electrons moving to the left as there are to the right there is no net current due to this motion. But if we connect the wire between the terminals of a power supply of potential difference V , an electric field is established in the wire that causes the electrons to move in response to this field. You may object that we previously said that the electric field inside charged metals is zero. But the circumstance here is different than before. There we put a quantity of charge on the metal and let the charges equilibrate under their mutual Coulombic interactions.
This field causes the electrons to accelerate (in direction opposite ). But in many of the scattering collisions the electrons lose their forward velocity acquired from that acceleration.

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## This note was uploaded on 03/12/2010 for the course PHY PHY taught by Professor Mueller during the Spring '09 term at University of Florida.

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Chapter 26 - Current, Resistivity, Resistance In our...

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