1
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Question

If radius of a resistor is decreased by 0.5% by stretching then percentage change in resistance

A
0.5%
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B
1%
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C
1.5%
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D
2%
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Solution

The correct option is D 2%Resistance of the resistor is given by,R=ρlA=ρl×AA×A=MassA2=Massπr4⇒R∝1r4Differentiating, we get, dR∝−4r5dr∴dRR=−4r51r4dr=−4drrHence, percent change in resistance is given bydRR×100=−4×drr×100Where dRR is change in resistance and drr is change in radius = -0.5% (here, decrease in radius is indicated by negative sign).dRR×100=−4×(−0.5)dRR×100=2%

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