Question

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter, the change in the resistance of the wire will be

• A. $200\%$
• B. $100\%$
• C. $50\%$
• D. $300\%$

Answer 1

The correct option is D $300\%$

Resistance $R=\frac{\rho l}{A}=\frac{\rho l^2}{V}$

here volume V is constant so $R\propto l^2$

thus, $\frac{R_2}{R_1}=\frac{(2l{)}^2}{l^2}=4$

% change in resistance $=\left[\frac{R_2-R_1}{R_1}\right]\times 100=[\frac{R_2}{R_1}-1]\times 100=[4-1]100=300$%