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ICSE Class 10 Answered

A wire of 9ohm having a lengh of 30 cm is tripled on itself  What is new resistance
Asked by lovemaan5500 | 13 Mar, 2018, 07:25: AM
answered-by-expert Expert Answer
There is an ambiguity in the question. Is it just tripling the length without changing cross section? or tripling the length with proportionally reducing the cross section by keeping the volume constant? normally when metal wire is stretched, cross section will be reduced. So i am giving the answer for both the cases.
 
(1) just tripling :- Resistance is directly proportional to length. hence if length is tripled resistance also tripled, i.e. 27 ohms.
 
(2) tripling with proportionate change in cross section :-
 
if volume remains constant, then L×A = (3L)×(A/3), where L and A are length and cross section respectively. When length is tripled Cross section reduced to (A/3). 
Hence new resistance Rn is given by
begin mathsize 12px style R subscript n equals rho space fraction numerator 3 L over denominator begin display style bevelled A over 3 end style end fraction space equals space 9 open parentheses rho L over A close parentheses space equals space 9 cross times R subscript o end style
Hence resistance increases by 9 times, i.e. 81 ohms
Answered by Thiyagarajan K | 13 Mar, 2018, 09:13: AM
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