Question

The length of a given cylindrical wire is increased by $150$%. Due to the consequent decrease in diameter the change in the resistance of the wire will be

• A. $200$%
• B. $525$%
• C. $300$%
• D. $400$%

Answer 1

The correct option is B $525$%

If suppose initial length, $l_1=100$, then
$l_2=100+150=250$
$\because \frac{R_1}{R_2}={\left(\frac{l_1}{l_2}\right)}^2={\left(\frac{100}{250}\right)}^2$
$\Rightarrow \frac{R_1}{R_2}=\frac{4}{25}\Rightarrow R_2=\frac{25}{4}{R}_1$
$\Rightarrow \frac{\Delta R}{R}\times 100=\frac{R_2-R_1}{R_1}\times 100$
$=\frac{\frac{25}{4}{R}_1-R_1}{R_1}\times 100=525$%