# HW5 - ECE 134 Introductory Field Theory Fall 2007 Reading...

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ECE 134 Introductory Field Theory Fall 2007 Reading Assignment: Cheng: Chapter 6 Cartoon Guide: Chapters 17-18 Homework #5 Due: Monday 5 November 2007 1) In this problem we will use a numerical PDE solver to explore the reduction in resistance due to a corner in a thin-film resistor as shown here. This is a very thin sheet of conducting material with contacts covering each end. Five squares of material are shown ( 2 w = A ). Find the true resistance, which is less than 5 sh r for reasons we discussed in class. From this, deduce the contribution of a corner. Include a plot of the equipotentials with your solution. Note that you will need to compute the total current by integrating the current density across the device width; one possible integration path is shown in the figure. This problem can also be solved analytically using a technique called conformal mapping, 0 y ∂Φ = 1 V Φ= 0 x ∂Φ = x y (0,0) (3,0) (2,1) (0,1) (2,3) 0 V Φ= A possible integration path for finding the current w w (3,3) 2 2 ln cosh 1 2 sh r R w π = + ⎝⎠ A (1.1)

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HW5 - ECE 134 Introductory Field Theory Fall 2007 Reading...

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