ch27-p046 - 46. The equivalent resistance in Fig. 27-55...

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If there were n +1 parallel resistors, then battery battery 1 eq 1 2 n VV n i R nR + + == + . For the relative increase to be 0.0125 ( = 1/80 ), we require i n+ 1 i n i n = i n+ 1 i n – 1 = (1 ) / (2 ) 1 /( 1) nn + + + = 1 80 . This leads to the second-degree equation n 2 + 2 n – 80 = ( n + 10)( n 8) = 0. Clearly the only physically interesting solution to this is n = 8. Thus, there are eight resistors in parallel (as well as that resistor in series shown towards the bottom) in Fig.
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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