Question

A certain wire has a resistance R. The resistance of another wire identical with the first except having twice its diameter is

• A. 2 R
• B. 0.25 R
• C. 4 R
• D. 0.5 R

Answer 1

The correct option is B 0.25 R

$A=\pi r^2$

$L^{\prime }=L$

$d^{\prime }=2d⟹r^{\prime }=2r⟹A^{\prime }=4A$

We know,

R $=\frac{\rho \times L}{A}$

Hence,

$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{L}{L}\times \frac{A}{4A}=\frac{1}{4}$

Hence,

$R^{\prime }=\frac{R}{4}$