Question

A wire X is half the diameter and half the length of a wire Y of similar material. The ratio of resistance of X to that of Y is

• A. 8 : 1
• B. 4 : 1
• C. 2 :1
• D. 1 : 1

Answer 1

The correct option is C 2 :1

Resistance of a wire is $R=\frac{\rho l}{\pi r^2}=\frac{\rho l}{\pi (d/2{)}^2}$ where $\rho =$ resistivity, $l=$length and $d=$ diameter of wire.
As both have same material so resistivity is same for both.
Thus, $R\propto \frac{l}{d^2}$

Here, $l_x=l_y/2$ and $D_x=D_y/2$

So, $\frac{R_x}{R_y}=\frac{l_x}{D_x^2}\times \frac{D_y^2}{l_y}=\frac{\left(l_y/2\right)}{(D_y/2{)}^2}\times \frac{D_y^2}{l_y}=\frac{4}{2}=\frac{2}{1}=2:1$