Anonymous
Anonymous asked in 科學其他:科學 · 1 decade ago

普通物理 的問題!! 請幫幫我!!

The pattern if resistors of equal value shown in the Fig. below

is repeated indefinitely. Show that the effective resistance between

terminals a and b is ( 1 + √3) R.

( Hint: Since the pattern in infinite , the resistance between points a'

and b' is the same as that between a and b.)

圖片參考:http://pic50.pic.wretch.cc/photos/48/m/michael393/...

請會的高手幫我的忙一下!!

謝謝!!!

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    Let the effective resistance between terminals a' and b' be r, then from the hints given in the question, we have:

    Effective resistance between terminals a and b = r

    r = 2R + (R//r)

    r = 2R + Rr/(R + r)

    Rr + r2 = 2R2 + 2Rr + Rr

    r2 - 2Rr - 2R2 = 0

    (r/R)2 - 2(r/R) - 2 = 0

    By quadratic formula, we have:

    r/R = {2 √[(-2)2 - 4(1)(-2)]}/2

    = 1 √3

    = 1 + √3 as resistance is impossible to be negative.

    Therefore r = (1 + √3)R

    Source(s): My physics knowledge
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