Electrons flowing through a metallic conductor will experience resistance. We\'l

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Electrons flowing through a metallic conductor will experience resistance. We'll explore a basic model to study the origin ot this resistance. Assume that we have a Block of metal with dimensions L W, and H. What is the kine-tie energy of a particular electron with velocity V = Vx, Vy, Vz ? Apply an electric field in the + x-direction (along the L dimension). This can be done by attaching a battery across the metal so that the current will flow along the + x-direction. The electric field will accelerate the electrons. What is the final kinetic energy of the electron in a) if it accelerates for a time t? The electrons in the metal will accelerate for some time l before it suffers a collision. During a collision it will lose the energy gained during the time interval t. Find this change in energy Delta U. This is energy that is lost between successive collisions. The initial velocity is random and is distributed equally in each direction. What is the average change in kinetic energy Delta U when averaged over all directions? The collision time will be random, but has an average value of r. The probability of finding the collision time between t and t + dt is given by theta - dt/tau. Thus, Delta U = x 0 Delta U. theta - dt/tau. Use your answer to part d) to show that the average energy lost per collision is given by ( Delta U = theta 2 2Ex tau2/me Suppose the density of electrons in the metal is n, and that the average collision rate is 1/r, what is the total energy lost per unit volume per unit time? Find energy lost per unit time (power lost) for the block of metal and compare it to the power dissipated in a resistor P = V2/R. Can you identify R? Discuss the dependence of R on the density of electrons, average collision time, and the dimensions of the metal block. Hint #1: x 0 x0 theta -x dx = m Hint #2: V = Ex L

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