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Question

# If a copper wire is stretched to make it 0.1% longer, the percentage change in its resistance is

A
0.2% increase
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B
0.2% decrease
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C
0.1% increase
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D
0.1% decrease
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Solution

## The correct option is A 0.2% increaseStep 1: New Area of the wireThe volume of the wire remains the same even after stretching.Vi=VfAl=A′l′Given that , l′=l+0.1%l=l+0.1100l=1.001l⇒A′=11.001AStep 2: Resistance of wireR=ρlA .....(2)R′=ρl′A′ .....(3)Dividing equation (3) by (2)R′R=l′AlA′⇒R′R=(1.001)2Using Binomial approximation(1+x)a=(1+ax) when ax<<1 (1.001)2=(1+0.001)2=(1+2×0.001)=1.002⇒R′=1.002RStep 4: Percentage increase in resistance of wireThus percentage increase in resistance=R′−RR×100 % =(1.002−1)×100 % =0.2%Hence option(A) is correct.

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