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From: Michael J. Schülke
Subject: Re: Complex number quiz
Date: Tue, 10 Sep 2002 14:04:20 +0200
References: <3D7DBD37.27C9BDEC@ipricot.com> <email@example.com>
X-Newsreader: MicroPlanet Gravity v2.50
> A string of resistors infinitely long thus:-
> 5R | 5R |
> \ \
> / 9R / 9R etc etc etc
> \ \
> / /
> 8R | 8R |
> The right hand side of the chain continues out of the window. What is the
> resistance measured on the left hand side ?
> You can't actually measure it because the electrons would take an infinitely
> long time to travel the circuit so you'll have to calculate it.
> Any takers ?
Let Z be the resistance of the chain. Since the chain is infinite,
taking away or adding one element at the front shouldn't make a
1 9R * Z
Z = 5R + ---------- + 8R = 13R + ------
1/9R + 1/Z 9R + Z
(Z - 13R) (Z + 9R) = 9R * Z
Z^2 - 13R * Z - 117 R^2 = 0
Z = 19.1 R
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