# HW5 - ECE 134 Introductory Field Theory Fall 2010 Reading...

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ECE 134 Introductory Field Theory Fall 2010 Page 1 of 2 Reading Assignment: Cheng: Chapter 6 Cartoon Guide: Chapters 17-18 Homework #5 Due: Monday 1 November 2010 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 ( ). Find the true resistance, which is less than 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; do this at a contact. This problem can also be solved analytically using a technique called conformal mapping, (1.1) Compare your numerical result against the exact formula (problems like this with known answers are helpful in debugging a program and establishing confidence in your numerical methods). Provide evidence of individual work.

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