Question

A resistive wire is stretched till its length is increased by $100$% due to the consequent decrease in diameter, the change in the resistance of a stretched wire will be _____

• A. $300$%
• B. $100$%
• C. $1250$%
• D. $50$%

Answer 1

The correct option is A $300$%

As we know,

$R=\rho \frac{l}{A}$

New length will be

$l^{\prime }=2l$

Due to increase in length , area must decrease as volume remains constant

$Al=A^{\prime }{l}^{\prime }=A^{\prime }\times 2l$

$A^{\prime }=\frac{A}{2}$

New resistance will be,

$R^{\prime }=\rho \frac{l^{\prime }}{A^{\prime }}=4\rho \frac{l}{A}$

So, change in resistance $=3\rho \frac{l}{A}$ or 300%