Question

A wíre of $1\Omega$ has a length of $1m$. It is stetched till its length increases by $25\%$. The percentage change in resistance to the neartest integer is :-

• A. $56\%$
• B. $25\%$
• C. $12.5\%$
• D. $76\%$

Answer 1

Answer: (A)

$R_0=1\Omega R_1=?$
${\ell }_0=1m{\ell }_1=1.25m$
$A_0=A$
As volume of wire remains constant so
$A_0{\ell }_0=A_1{\ell }_1\Rightarrow A_1=\frac{{\ell }_0{A}_0}{{\ell }_1}$
Now
Resistance $(R)=\frac{\rho \ell }{A}$
$\frac{R_0}{R_1}=\frac{{\ell }_0/A_0}{\rho {\ell }_1/A_1}$
$\frac{1}{R_1}=\frac{{\ell }_0}{A_0}\left(\frac{{\ell }_0{A}_0}{{\ell }_1\times {\ell }_1}\right)R_1=\frac{{\ell }_1^2}{{\ell }_0^2}=1.5625\Omega$
So $\%$ change in resistance
$=\frac{R_1-R_0}{R_0}\times 100\%$
$=\frac{1.5625-1}{1}\times 100\%$
$=56.25\%$