Question

Resistance of a wire is $20\, ohm$, 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
$A_{1} l_{1} =A_{2} l_{2}$
$A_{1} l =A_{2} \times 3 l$
$A_{2} =\frac{A_{1}}{3}$
Ratio of resistance
$\frac{R_{1}}{R_{2}}=\frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}}$
$=\frac{l}{3 l} \times \frac{1}{3}=\frac{1}{9}$
$\frac{20}{R_{2}}=\frac{1}{9}$
$\Rightarrow R_{2}=180\, \Omega$