Question

A wire $X$ of half the diameter and half the length as of a wire $Y$ of similar material. The ratio of resistances 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 $2:1$

We know that,

$R=\rho \frac{l}{A}=\rho \frac{4l}{\pi d^2}$

As material is same, $R\propto \frac{l}{d^2}$

So,

$\frac{R_X}{R_Y}=\frac{l_X{d}_Y^2}{l_Y{d}_X^2}$

$\Rightarrow \frac{R_X}{R_Y}=\frac{\left(l/2\right)d^2}{l(d/2{)}^2}=\frac{1}{1/2}=2:1$

Hence, option $\left(C\right)$ is the correct answer.