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4. A 10 ohm thick wire is stretched so that its lengthbecomes three times. Assuming that there is nochange in density on stretching, calculate the resistanceAns 90 ohm]of the new wire. |
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Answer» Resistance ‘R = 10 ohm’ is related to length ‘L’, area of cross-section ‘A’ and resistivity ‘ρ’ as,R = ρL/AWhen L is tripled ,As we know that the volume of the wire remains same.old volume = new volumeAL = A'L' ....(i) ( as volume = area x length )L' = 3LSo, from (i)A' = A/3So the new resistance is ,R' = ρL'/A'orR' = ρ(3L)/(A/3) = 9 (ρL/A)=> R' = 9Rso, the new resistance increases nine fold.Now,R' = 9 x 10ohmsthus,R' = 90 ohms |
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