Question

The x% change is brought in length of a wire, its resistance will change by:

• A. x/2%
• B. 2x%
• C. 3x%
• D. 4x%

Answer 1

The correct option is B 2x%

Resistance of the wire $R=\frac{\rho l}{A}$ where $A=V/l$

$⟹R=\frac{\rho l^2}{V}$

$\therefore$ Percentage change in resistance $\frac{\Delta R}{R}\times 100=\frac{2\Delta l}{l}\times 100$ ($\because V,\rho =constant$)

GIven : $\frac{\Delta l}{l}\times 100=x$

Percentage change $\frac{\Delta R}{R}\times 100=2x$ %