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CBSE Class 10 Answered

A conductor has a length of 2 0 m and a radius of 3 0 mm If the resistance is R= 100Ω, calculatethe new resistance if the same material has: (a) length=6 0 m and r=6 0 mm (b) length=1 0m and r=1 0mm ... If the resistance is R=100Ω, calculate the new resistance if the same material has: ...  (a) length = 6.0m and r=6.0mm(b) length=1.0m and r= 1.0mm.
Asked by bcnandi | 12 May, 2019, 02:14: PM
answered-by-expert Expert Answer
Resistance is directly proportional to length l  of wire and inversely proportional to area.
Since area is prportional to square of radius r, Resistance is inversely proportional to square of radius r.
 
Hence we write resistance as K×l/r2 where K is constant.
 
Resistance R of wire of 6 m length and 6 mm radius :-  begin mathsize 12px style R over 100 equals fraction numerator begin display style K cross times bevelled 6 over 36 end style over denominator begin display style K cross times bevelled 2 over 9 end style end fraction space equals space 0.75 end style  or  R = 75 Ω
 
Resistance R of wire of 1 m length and 1 mm radius :-  begin mathsize 12px style R over 100 equals space fraction numerator begin display style K cross times bevelled 1 over 1 end style over denominator begin display style K cross times bevelled 2 over 9 end style end fraction space equals space 4.5 end style   or  R = 450 Ω
 
 
Answered by Thiyagarajan K | 12 May, 2019, 02:55: PM

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