Question

Resistance of a wire is $20ohm$, it is stretched upto, three times of its length, then its new resistance will be :

• A. $6.67\Omega$
• B. $60\Omega$
• C. $120\Omega$
• D. $180\Omega$

Answer 1

Answer: (D)

Wire is stretched, therefore its volume remains unchanged
$A_1{l}_1=A_2{l}_2$
$A_{1}l=A_2\times 3l$
$A_2=\frac{A_1}{3}$
Ratio of resistance
$\frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}$
$=\frac{l}{3l}\times \frac{1}{3}=\frac{1}{9}$
$\frac{20}{R_2}=\frac{1}{9}$
$\Rightarrow R_2=180\Omega$