A copper wire is stretched to make it 0.5 %$ longer.

Question:

A copper wire is stretched to make it $0.5 \%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

  1. (1) $2.0 \%$

  2. (2) $2.5 \%$

  3. (3) $1.0 \%$

  4. (4) $0.5 \%$


Correct Option: , 3

Solution:

(3) Resistance, $R=\frac{\rho \ell}{A}$

$\mathrm{R}=\rho \frac{\ell}{\mathrm{A}} \times \frac{\ell}{\ell}=\frac{\rho \ell^{2}}{\mathrm{~V}}[\because$ Volume $(\mathrm{V})=\mathrm{A} \ell .]$

Since resistivity and volume remains constant therefore $\%$ change in resistance

$\frac{\Delta \mathrm{R}}{\mathrm{R}}=\frac{2 \Delta \ell}{\ell}=2 \times(0.5)=1 \%$

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now