ECE 134
Introductory Field Theory
Fall 2010
Page 1 of 2
Reading Assignment:
Cheng:
Chapter 6
Cartoon Guide: Chapters 1718
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 thinfilm 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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 Fall '08
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 Magnetic Field

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