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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  • Dixon
    Lv 7
    7 months ago
    Best 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

  • Anonymous
    7 months ago

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

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