Question

If a wire is stretched to make it $0.1\%$ longer, its resistance will:

• A. Increase by $0.2\%$
• B. Decrease by $0.2\%$
• C. Decrease by $0.05\%$
• D. Increases by $0.05\%$

Answer 1

The correct option is A Increase by $0.2\%$

$LetinitiallengthbeL.L^{\prime }betheincreasedlength.Accordingtoqquestion,L^{\prime }=L+\left(\frac{0.1}{100}\right)L=1.001LSoInitialvelocityV=Newvoulme{V}^{\prime }{V}^{\prime }=V=>A^{\prime }\times L^{\prime }=A\times L{A}^{\prime }=\frac{AL}{1.001L}=\frac{A}{1.001}{R}^{\prime }=\rho \frac{L^{\prime }}{A^{\prime }}=\rho \times \frac{1.001L}{\left(\frac{A}{1.001}\right)}=\rho \times \frac{{L(1.001}^2)}{A}=1.002R$

Percentage = $\frac{1.002-1}{1}\times 100=0.2$ %