# infinite resistors problem?

The network shown to the right consists of a infinitely-repeating pattern of resistors, all with a resistance of 1Ωconnected to a 12V battery with negligible internal resistance. Find the current measured by the ammeter. [Hint: How is the circuit to the right of points A and B different from the circuit connected to the battery?]

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- DixonLv 77 months agoBest Answer
R = 1 + (1 II R) + 1 . . . . . After this it's just mathematics.

R = 2 + R/(R + 1) . . . . . . .(parallel value by product over sum)

R(R + 1) = 2(R + 1) + R

R² + R = 2R + 2 + R

R² - 2R - 2 = 0

...

R = 1 + √3

etc

- Anonymous7 months ago
See Q5 (similar problem + solution) here: http://www.apphysicsresources.com/2010/07/

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